Boot Problem

I have a Compag computer with Win ME installed that will lock up after being on for a while. This is not caused by heat as the cpu is cool with a good fan. Also when trying to boot Especially after a freeze, the post won’t do anything. The power comes on, fans start, HD spins then nothing. Monitor stays amber. After much plugging and re-plugging or after a long rest period (as in days), It reboots perfectly, but freezes again after a while. Any suggestions?