Your description of the problem is a bit confusing, because you mix up three things in it:
1. BSOD
2. No boot-up.
3. No image on screen.
I did not get a clear understanding which problem happened when, except that none of them were reproducible at your friend's or the comp shack. Each of these can have multiple reasons, so you have a real mess there
I agree with the previous posters that probably the wiring in your house is part of the problem in case the computer does not start up at all. Try out several plugs while using no other equipment in the same room (including the monitor! only keyboard and mouse allowed). And check the power cable and connectors.
Only once the computer is running (and maybe you've figured out the "perfect plug"), plug in the monitor, but check all cables and plugs first. If it does not show anything, plug in a different monitor. Then the first monitor with a different cable. Then the second monitor with the second cable. Note what works and what does not.
In cases like yours, you have to be very systematic. Only change one factor (power outlet, cables, monitor) at a time. By doing so, you should be able to figure out what causes the problems.
Only if none works reliably I would open the case and make sure that each part is firmly sitting in its place - graphics card, power connectors, RAM, CPU, fans. I don't think heat is the problem, since if it was, your computer would not be able to run for several hours straight.