i would check to see if there is crud shorting out some pins on the mainboard. check around the fine pins of the FPGA chips and CPU. crap dirt buildup on these chips can cause corrosion,shorts, and general randomness.
check your voltages. your 5 volts should be at least 5.0 to 5.2 or something like that. check your 12v as well... anywhwere from 11.5 to 12.5 ... or whatever is usually fine. if you have a read board...your 3.3 should be damn close to 3.3 volts.
also check these voltage with your meter set to AC. while it runs, you should have less than 30mv AC ripple in your 5v (and 3.3 if applicable) DC if it's up in the 100 or more, your power supply is putting too much noise in the system and needs to be replaced. ripple in your DC power can cause all kinds of randomness.
hold down the start button and power on the system... it should enter a test mode where you can do some rudimentary tests and see if there is something obvious going on through there