If it's stopping at the RAM-check stage, it's not even reading the HDD, is it? There's still a load of POSTing and BIOS passing to do before that point.
If you're having an issue before you even get to booting the OS, there are two possibilities: hardware error, or incorrect BIOS settings. If it's the former it'll be a pig to diagnose, but I'd try swapping the RAM for a start. Either way, the first thing I'd do is reset the BIOS (there should be a jumper near the CMOS battery or, if it comes to it, you can just remove the battery for a minute). If that solves the problem then have a look in the BIOS and set it up properly. If it doesn't, your hardware's properly knackered somewhere - whether RAM, CPU or motherboard. If you want to diagnose properly you'll need another rig to swap bits out of.