This guide may well be worth having a look through:http://www.tomshardware.co.uk/forum/261145-13-perform-steps-posting-boot-video-problems
I know it primarily applies to new-builds but the same troubleshooting techniques usually apply.
Remove everything that isn't essential - HDDS, GPU (if you have onboard graphics), DVD Drives etc. and then try booting. You only need the RAM, CPU and Mobo to POST and boot so this will eliminate (or help locate) potential faulty components.
Not sure if it's in the guide or not but have you tested the RAM with MemTest86? You can also try removing one stick and see if the problem persists. Then swap with another stick and repeat. Try this in each and every RAM slot. The only thing is if the system is that old you may only have the one stick.