Can anyone help with these kernel panics?

Question

I work for the NHS.  Have spent most of my salary on Adobe Premiere Pro using a Intel Core Mac OS 10.5.8 which is supposed to be enough for the system requirements.  Have spent all day shutting down my computer unable to start the software.  If it does start it freezes and tells me to restart.  This is not acceptable.  Can anyone help??? Adobe cefrtai nly don't want to is there ahtyone out there with any solutions?  I ahve checked the hard drive it is fine, have done all the usual checks to no avail. Cannot find anywhere to talk to Adobe, their website is a minefield of Groundhog Day!
I have the same problem with Photoshop purchased last year as part of a creative package.  This is really annoying!

Answer 1

Dear Wonderspark,
I am back at my iMac.  Here are the details of my hardware.
Model Name:
iMac
  Model Identifier:
iMac7,1
  Processor Name:
Intel Core 2 Duo
  Processor Speed:
2.4 GHz
  Number Of Processors:
1
  Total Number Of Cores:
2
  L2 Cache:
4 MB
  Memory:
3 GB
  Bus Speed:
800 MHz
  Boot ROM Version:
IM71.007A.B03
  SMC Version (system):
1.20f4
  Serial Number (system):
W88035L3X86
  Hardware UUID:
00000000-0000-1000-8000-001EC205D8B9
Chipset Model:
ATI,RadeonHD2600
  Type:
Display
  Bus:
PCIe
  PCIe Lane Width:
x16
  VRAM (Total):
256 MB
  Vendor:
ATI (0x1002)
  Device ID:
0x9583
  Revision ID:
0x0000
  ROM Revision:
113-B2250F-219
  EFI Driver Version:
01.00.219
  Displays:
iMac:
  Resolution:
1680 x 1050
  Depth:
32-Bit Color
  Core Image:
Hardware Accelerated
  Main Display:
Yes
  Mirror:
Off
  Online:
Yes
  Quartz Extreme:
Supported
  Built-In:
Yes
The software versionas are as follows.
Adobe Photoshop CS5 version 12.0.4
Adobe Premiere Pro CS 5.5 version 5.5.0
I hope that is more use.  As I said, the software is successfully installed, but I cannot open Premiere Pro.  Photoshop does open occasionally but rather like Russian roulette.
I also have the Creative suite and Dreamweaver is no problem, neither is Indesign.  This makes no sense to me I would be grateful for any help.  I have checked the hardware and the system is ok.  I have tried re-installing the software after un-installing it but that made no difference.  I obviously have turned the machine on and off because of the black veil that descends upon the screen during the kernel panic.  Premiere Pro has alo frozen everything rather than causing a panic too. HELP!