Having had a quick look at the spec for your computer I do not think it has onboard graphics, so unfortunately you cannot disconnect that ATi card from the AGP slot to test with the onboard graphics.
But you say you cannot run the diagnostics.
What is the sequence of leds on boot.
If you cannot enter setup - you have I think a serious hardware fault somewhere as the setup ie enter BIOS is not dependant on the state of the hard drive.
I suggest you try setup with the HDD disconnected.
I would also try another keyboard.
If still no success I would see if you can try another graphics card
Check ram, although I do not think it is that, if you have two sticks, take one out, leave the first slot populated and then swap the sticks.
If you can still boot to that Barts and the hard drive is seen run a check on the hard drive.
It is the lack of ability to enter setup that concerns me - it is either keyboard or hardware error.
The earlier blue screen was of course the warning - but that info is pretty useless now.
I asked earlier about your data and as puppy runs in ram it will effectively test your hardware for you.
No, my computer has not been making any funny noises, though my CD drive is temperamentally noisy, but this has been the case for a long time.
A long shot but try boot with the optical drive disconnected.