The Dell Inspirion 5100 is a pretty old laptop from 2003. I used to have one, but it would run very hot because of the Pentium 4 desktop processor. It is known to have an "overheating problem." Most likely the video card or motherboard is damaged that is why it is shutting down or not turning on.
If you can't boot into BIOS, only get a black screen, and cannot hear Windows loadup, then the best solution is to just buy a new laptop because fixing the Dell Inspirion 5100 would cost about the same. There is no simple solution to this problem.