Sometimes my computer will not start-- it makes a beeping noise four times at which point it takes a 2.5 second pause and then starts the routine again. It's been plaguing me for about a month or so. Also, sometimes it crashes with random jumbles of pixels in rectangles on the screen, then freezes. Is there any solution to this?

From your description I would blame the VGA.

Award Bios -

4 beeps (1- long,3-short) usually indicates Video Card Error

The beeps are one second long. The pattern is BEEP -- BEEP - BEEP - BEEP --- BEEP - BEEP and stops. Dwo dashes indicate 1 second, one indicates half, and 3 indicate 1.5-2

Strip your system, leave only the Processor and Heatsink. with powersupply.
No Ram, No Usb pheriperals, no PCI, no VGA, No nothing.

What do you get?

you want to hear one single beep.

Yeap, from your expaination, there has to be some problems with VGA..

you want to hear one single beep.

Correction you want to hear a couple of beeps in a consecutive manner.

4 or 5 evenly spaced beeps.