Mac Pro 1,1 Help Needed

Question

I’ve been having a few problems with my Mac Pro 1,1 for a while now.  The graphics card appeared to be the cause of the last issue (lines of garbled pixels appearing across the screen), the screen going to black once or twice and not letting me do anything other than a hard reset.
Side note: not long after I bought the machine in 2006 I remember it wouldn’t run The Sims 3 without it having major crashing issues (black screen but sound still playing underneath).
I changed my graphics card about a month ago to the ATI Radeon 5770.  Installation was fine and everything seemed to work ok (although, the second DVI connection doesn’t work with either the Apple Cinema HD display, or my HD monitor, so I have one plugged in to DVI 1 and the other in to the mini display port).  The other problem with this is that (and this is the only game I have to test it on) is that GTA San Andreas still freezes forcing me in to a hard reset situation.  But other video intensive apps (Final Cut Pro for example) works fine.
I used the snow leopard disk to do a disk repair but that found no issues.  I repaired the disk permissions as well.  This appeared to fix nothing.
I few other issues I’ve had recently:
The Finder crashes.
The computer hangs on a restart / shut down.
USB ports don’t always work on system start.  I have to unplug the mouse and/or the keyboard and plug them back in again to get them to work.  Some of these are on the back of the tower and others are in the back of the monitor.
Disk drive can’t read burned discs.
When ejecting optical disks the icon will either go semi-transparent and then stay that way (this is usually the case, especially after the disc has been in use).
Other times when I try and eject the disc the disc unmounts, but the tray doesn’t open.  Then the disc and the drive itself goes missing from disk utility and can’t be remounted without a hard reset.
The last issue that moved me in to doing a fresh install was Final Cut not working at all.  I’ve since reinstalled but the same problems persist - the optical drive not ejecting (but disappearing from the system leaving me unable to do anything other than a hard reset to get it back).  This causes obvious problems when I’m installing multi-disk systems.
After I restarted, before I did anything else with it, I asked it to run system update which it did and found updates.  I downloaded and installed these and then it restarted.  It shut down fine, and appeared to start up fine.  But then the Finder crashed and while the mouse cursor moved around, the keyboard wouldn’t input any commands and I couldn’t actually click on anything - another hard reset.
I’m starting to get to the end of my tether with my “superior” mac experience.  I know it’s easy to suggest it must be the graphics card causing this, but some of these issues have happened in the past, just not as frequent as now, so I’m hoping there are some ideas that go above the “change graphics card” idea.  Of course, I am open to this being the cause.
I’ve ran Onyx & Rember and both have been successful.
Any ideas you wonderful lot?
While I imagine the obvious answer is "take it to a repair centre" this isn't an easy option where I live as all official Apple stores (i.e. not premium resellers) are quite a distance.
Stats are below:
Model Name:          Mac Pro
  Model Identifier:          MacPro1,1
  Processor Name:          Dual-Core Intel Xeon
  Processor Speed:          2.66 GHz
  Number Of Processors:          2
  Total Number Of Cores:          4
  L2 Cache (per processor):          4 MB
  Memory:          6 GB
  Bus Speed:          1.33 GHz
  Boot ROM Version:          MP11.005C.B08
  SMC Version (system):          1.7f10
  Serial Number (system):          CK******UPZ
ATI Radeon HD 5770:
  Chipset Model:          ATI Radeon HD 5770
  Type:          GPU
  Bus:          PCIe
  Slot:          Slot-1
  PCIe Lane Width:          x16
  VRAM (Total):          1024 MB
  Vendor:          ATI (0x1002)
  Device ID:          0x68b8
  Revision ID:          0x0000
  ROM Revision:          113-C0160C-155
  EFI Driver Version:          01.00.436
  Displays:
HP ZR2440w:
  Resolution:          1920 x 1200
  Pixel Depth:          32-Bit Color (ARGB8888)
  Display Serial Number:          CNT13400TQ 
  Mirror:          Off
  Online:          Yes
  Rotation:          Supported
Cinema HD:
  Resolution:          1920 x 1200
  Pixel Depth:          32-Bit Color (ARGB8888)
  Display Serial Number:          2A6431YTUG0
  Main Display:          Yes
  Mirror:          Off
  Online:          Yes
  Rotation:          Supported
Display Connector:
  Status:          No Display Connected
Memory Slots:
  ECC:          Enabled
DIMM Riser A/DIMM 1:
  Size:          2 GB
  Type:          DDR2 FB-DIMM
  Speed:          667 MHz
  Status:          OK
  Manufacturer:          0x802C
  Part Number:          0x3138484632353637324A4436363745314434
  Serial Number:          0xDF3E7A28
DIMM Riser A/DIMM 2:
  Size:          2 GB
  Type:          DDR2 FB-DIMM
  Speed:          667 MHz
  Status:          OK
  Manufacturer:          0x802C
  Part Number:          0x3138484632353637324A4436363745314434
  Serial Number:          0xDF3E7A34
DIMM Riser B/DIMM 1:
  Size:          512 MB
  Type:          DDR2 FB-DIMM
  Speed:          667 MHz
  Status:          OK
  Manufacturer:          0x80AD
  Part Number:          0x48594D5035363441373242503844322D5935
  Serial Number:          0x50260008
DIMM Riser B/DIMM 2:
  Size:          512 MB
  Type:          DDR2 FB-DIMM
  Speed:          667 MHz
  Status:          OK
  Manufacturer:          0x80AD
  Part Number:          0x48594D5035363441373242503844322D5935
  Serial Number:          0x50260005
DIMM Riser A/DIMM 3:
  Size:          512 MB
  Type:          DDR2 FB-DIMM
  Speed:          667 MHz
  Status:          OK
  Manufacturer:          0x80AD
  Part Number:          0x48594D5035363441373242503844322D5935
  Serial Number:          0x50260008
DIMM Riser A/DIMM 4:
  Size:          512 MB
  Type:          DDR2 FB-DIMM
  Speed:          667 MHz
  Status:          OK
  Manufacturer:          0x80AD
  Part Number:          0x48594D5035363441373242503844322D5935
  Serial Number:          0x50262006
DIMM Riser B/DIMM 3:
  Size:          Empty
  Type:          Empty
  Speed:          Empty
  Status:          Empty
  Manufacturer:          Empty
  Part Number:          Empty
  Serial Number:          Empty
DIMM Riser B/DIMM 4:
  Size:          Empty
  Type:          Empty
  Speed:          Empty
  Status:          Empty
  Manufacturer:          Empty
  Part Number:          Empty
  Serial Number:          Empty
<Edited by Host>

Answer 1

Please read this whole message before doing anything.
This procedure is a test, not a solution. Don’t be disappointed when you find that nothing has changed after you complete it.
Step 1
The purpose of this step is to determine whether the problem is localized to your user account.
Enable guest logins and log in as Guest. For instructions, launch the System Preferences application, select Help from the menu bar, and enter “Set up a guest account” (without the quotes) in the search box.
While logged in as Guest, you won’t have access to any of your personal files or settings. Applications will behave as if you were running them for the first time. Don’t be alarmed by this; it’s normal. If you need any passwords or other personal data in order to complete the test, memorize, print, or write them down before you begin.
Test while logged in as Guest. Same problem(s)?
After testing, log out of the guest account and, in your own account, disable it if you wish. Any files you created in the guest account will be deleted automatically when you log out of it.
Note: If you’ve activated “Find My Mac” or FileVault in Mac OS X 10.7 or later, then you can’t enable the Guest account. Create a new account in which to test, and delete it, including its home folder, after testing.
Step 2
The purpose of this step is to determine whether the problem is caused by third-party system modifications that load automatically at startup or login.
Disconnect all wired peripherals except those needed for the test, and remove all aftermarket expansion cards. Boot in safe mode and log in to the account with the problem. The instructions provided by Apple are as follows:
Be sure your Mac is shut down.
Press the power button.
Immediately after you hear the startup tone, hold the Shift key. The Shift key should be held as soon as possible after the startup tone, but not before the tone.
Release the Shift key when you see the gray Apple icon and the progress indicator (looks like a spinning gear).
Safe mode is much slower to boot and run than normal, and some things won’t work at all, including wireless networking on certain Macs.
The login screen appears even if you usually log in automatically. You must know your login password in order to log in. If you’ve forgotten the password, you will need to reset it before you begin.
Test while in safe mode. Same problem(s)?
After testing, reboot as usual (i.e., not in safe mode) and verify that you still have the problem. Post the results of steps 1 and 2.