Please Help :( iMac 20" refuses to boot up with anymore than 1gb ram?

Question

Please Help iMac 20" refuses to boot up with anymore than 1gb ram?  It was fine 4 days ago and had been working with a 1gb stick in one slot and a 2gb stick, which had replaced the orignal 1gb stick that I got it with, in the other and it had shown 3gb of ram and was working just fine with that since November?  It went to sleep briefly 4 days ago while I was waiting on a customer and I came back to try to wake it up and it never would forcing me to hard boot it.  When I did that it would only go to a black screen with a solid white light on the power indicator.  Over and over again and same thing.  I read and tried every suggestion I could possibly find in this and a few other mac forums to no avail.
I finally after reading about RAM issues etc.  I decided to power off and take out the ram sticks and try them one at a time in each slot.  So I took out the 2gb stick and did the SMC reset and it would boot up and work just fine with the 1 gb of ram.  So then I went through the same process with the 2gb stick and it would not boot up only go to a black screen with white solid light again (NOT flashing).  So then I tried the other original 1gb I had replaced with the 2gb and it worked just find like the other 1gb.  So then I tried just 1gb stick in the other ram slot (back facing one) and with just the 1gb strip it booted up and worked fine.  Tried it with the other 1gb stick and once again that one too worked just fine.  So I determined it wasn't the slot itself I thought?  I then tried the 2gb in the back slot and it would not boot only go to the black screen white solid light deal like before.  So I thought well ok it's obviously the 2gb ram must have somehow went bad (even though I have only had it since November) and I thought well I will just use the (2) 1gb sticks in each slot and then that will at least give me 2gb because only 1gb really ***** LOL.  So I proceeded to go through the same shut down process installed both sticks (I always push them to I feel them click and my fingers have a nice indention on them) reset the SMC and turned the power one and.... It would only go to the black screen with white solid light on power indicator????  I went through the same above process at least 3 times and again today a few times and I can't figure it out and I tried to search and search and I couldn't find anything like what I am experiencing.....What happened?  Please help this slow Imac is killing me.  It will work with 1gb ram only nothing more?  Here are the specifics of my Imac.
It is a 20" Late 2006 Intel Core 2 Duo 2.16 ATI Radeon X1600 256 MB graphics card and Ram with now only 1gb (did have 3gb) and I am running OSX Lion 10.7.5
When I go to system report and go under memory it shows this:
BANK 0/DIMM0:
  Size:          1 GB
  Type:          DDR2 SDRAM
  Speed:          667 MHz
  Status:          OK
  Manufacturer:          0xCE00000000000000
  Part Number:          0x4D342037305432393533435A332D43453620
BANK 1/DIMM1:
  Size:          Empty
  Type:          Empty
  Speed:          Empty
  Status:          Empty
  Manufacturer:          Empty
  Part Number:          Empty
  Serial Number:          Empty
Any help I can get would really be appreciated.  Thanks in advance
ALSO...Here is also a pic of the system log right before it happened.  It even changed the date to 07/2014????
I have some more if needed??????????????? 
<Personal Information Edited by Host>

Answer 1

The Memtest just completed and came back like this?  It only test the single 1gb chip because anything more in this computer it won't go past the black screen with solid white power light. 
Memtest version 4.22 (64-bit)
Copyright (C) 2004 Charles Cazabon
Copyright (C) 2004-2008 Tony Scaminaci (Macintosh port)
Licensed under the GNU General Public License version 2 only
NOTE: No command-line arguments have been specified
Using defaults: Test all available memory, one test pass, no logfile
Mac OS X 10.7.5 (11G63) running in multiuser mode
Memory Page Size: 4096
System has 2 Intel core(s) with SSE
Requested memory: 250MB (263086080 bytes)
Available memory: 250MB (263086080 bytes)
Allocated memory: 250MB (263086080 bytes) at local address 0x0000000101000000
Attempting memory lock... locked successfully
Partitioning memory into 2 comparison buffers...
Buffer A: 125MB (131543040 bytes) starts at local address 0x0000000101000000
Buffer B: 125MB (131543040 bytes) starts at local address 0x0000000108d73000
Running 1 test sequence... (CTRL-C to quit)
Test sequence 1 of 1:
Running tests on full 250MB region...
  Stuck Address       : ok             
  Linear PRN          : ok             
Running comparison tests using 125MB buffers...
  Random Value        : ok
  Compare XOR         : ok
  Compare SUB         : ok
  Compare MUL         : ok
  Compare DIV         : ok
  Compare OR          : ok
  Compare AND         : ok
  Sequential Increment: ok
  Solid Bits          : ok             
  Block Sequential    : ok                
  Checkerboard        : ok             
  Bit Spread          : ok               
  Bit Flip            : ok               
  Walking Ones        : ok               
  Walking Zeroes      : ok               
All tests passed!  Execution time: 362 seconds.
logout
[Process completed]
Seems Okay I guess?