I have a feeling you may have faulty ram.Just to verify this,can you download Memtest from a working pc
Memtest bootable (direct download ) click here
Save to your desktop
Then burn using Imgburn click here or Something that burns iso images..If you have Nero,this should work also.
Now im banking on your bios is already set to boot from cd as opposed to hdd (as you cannot get access to the bios).
When you first switch on the problem computer,open the cd drawer and place the Memtest boot cd in and close the drawer and reboot the computer.
Im now hoping the the bios is set to boot from cd,if this is-you will Memtest at work,let this run for at least 10 steps.