L20 197 model (celeron) laptop.

In 19 years of working on computers I've seen 1 bad Intel CPU and it still worked it just showed the wrong processor speed. I'd eliminate the CPU being the problem. Generally if you have a bare system with motherboard, ram, keyboard and video and they turn on the system is good. The video may cause a crash if it's bad somewhere in the bootup process going into windows but it shouldn't stop the initial bootup process. The area I would likely suspect is the hard drive. If the arm inside the drive that controls the heads is loose it can cause the drive to read sometimes when cool and then to start slipping and not read when the system is warmer. If you can get into the bios there should be someplace there to check your temperatures and voltages. Those might be a suspect area. If the power supply isn't delivering the proper voltages or the CPU is getting hot could cause problems also. I'd like to hear more about what you're seeing on the screen when this system fails to boot. Does is show the ram countup, system devices and hard drives as detected in the bootup process? Or is the screen just blank. When it doesn't boot does the hard drive light blink continuously?