possible problems and solutions:
1. processor overheating (most likely)
open cpu case, check if the fan is running. if not, plug it out, clean it, put it back again. if yes, see if you need thermal paste.
2. memory probs
www.memtest86.com/
self explanatory. its a prog which tests your ram. run 5 passes for optimal diagnostics. if ram is faulty, replace it. if ram is fine, then it maybe windows. but i doubt it since you say that you cant boot up the pc later. try a fresh install of windows, but if it crashes during the install itself, its not the problem then.
3. power supply
bad power supply = bad computer.
5. motherboard problems like shorted/open capacitor etc
for all the hardware problems take your cpu to a friends place, and try your components one by one on his comp. whichever is faulty, can be identified easily.
offtopic, good to be on the forum again

i think i've got the least no of posts for being in here for four years