depends on how evil you want to be... and what sort of problems?
An interesting one is always a faulty cable, Power/Network. For a nasty hardware fault, dig out some old 266mhz ddr & drop it in a nice new board at 400fsb

If you've got a PC with on board VGA & a graphics card, disable the onboard in bios, then plug the monitor into the on-board...
Could always drop the hdd, and ask them to identify the problematic component... anyone really competent should be able to tell a dodgy hdd by ear from 6ft
I guess it depends on your company policy, where I work we tend to check the basics, Screen/Cables/Peripherals and any software/bios options... If its an obvious hardware fault, like HDD... then we'll replace the disk, otherwise its just scrap the machine, and give it to some kid who'll spend a week troubleshooting it
