I would suggest that the RAM is a likely culprit. I have encountered similar circumstances in the past, and more often than not, RAM has been the cause. If you can get hold of a single RAM module which you know works reliably, try booting with just that installed. Some motherboards are also very fussy about the type of RAM and the BIOS memory settings. I had an ASUS board a while back which i tried 3 different brands of ram before i found one which would allow booting into BIOS. Once there I was able to manually set the RAM setting to the proper defaults and from then I had no problem with any type of RAM, even the ones which wouldn't work earlier.
If does not solve your problem, I suggest pulling the computer completely appart, then reconstructing it with a bare minimum needed for boot, i.e. just one stick of RAM, and leave out any extra expansion cards such as sound and network cards.
Sometimes the problem is as simple as a component not seated correctly.
Good Luck.