You could try backing up your data (boot from floppy and copy files to the D drive for instance), then a fresh install of ME including formatting the drive. Normally a re-install over the top doesn't sort out problems like yours, but a completely fresh install will. You could do a "quick" format, which will essentially erase the data.
If the system still crashes after the hard disk has been formatted (ie during or after windows install) you probably have a hardware problem, and my guess would be the memory. You could try removing it, and re-inserting and see if it makes any difference, or try a different memory slot, or if you can get you hands on some spare memory, try that. Hard disk errors normally manifest themselves in strange file names (ie a file called pic.jpg might show up as $%%$3pic.jpg or something), bad sectors reported by Windows / Scandisk etc. If you hard disk really is bad, Windows may not install at all, not even getting past the "checking your hardware (or whatever bit it is)" part.
If you know.....is your hard disk serial ATA or a standard IDE device? Sometimes the SATA if not corectly configured in the Bios could cause symptoms such as yours. Also do you get any Windows "blue screen of death" STOP type errors? If you do, write down the msg and code (ie 0x000035353) as they can often point to what is causing the problem.
EA
In reply to your last part:
Motherboard drivers,
Graphics card,
modem,
printer,
virus checker,
Then if you have broadband, do a Windows update.