Problem with girlfriend's computer - motherboard issue?

[Deadbeat]

My girlfriend's computer has gone up the duff at last and I'm not sure what the issue is - hoping you guys can shed some light on the issue. Here's her description:

My computer has had a problem before in that it will be running fine for the evening, but every now and again when i go to turn it on again in the morning it will turn on (in that the fans and all the LEDs light up) however it doesn’t appear to boot up. The monitor will read no signal detected. In the past i have just turned it off and on again a few times and it has worked again, not this morning however, this time it acted in the same way, working fine last night but after accidently leaving my computer on during the night it was running very slowly so turned it off (held power button in bad me) and after a couple of minutes went to turn it on again and nothing...spent a fruitless day where i played with cycling the power, testing the ram slots and actually after moving the ram position once managed to get the computer to start booting but it got to a certain point while still on black screen where it told me could not boot from disk, insert disk and try again.

Might be unrelated but:

Have regularly had a problem with the computer turning immediately off after being powered on and immediately rebooting itself.

Used to have a problem with it blue screening, tested several options and eventually replaced ram and hard drive.

Seems like a motherboard issue to me, but I'm not sure. The motherboard and CPU are the only bits that aren't relatively new - they came out of a bits collection of a friend of hers and are a few years old. Everything else from the graphics card to the RAM is about a year old or less. Anybody know what to replace, or how to test?

 

[Deadbeat]

The motherboard is an abit IP35, socket 775 - processor is unknown. If it's a BIOS issue, how can I fix that without being able to boot up the computer?