Well, you should be able to enter the bios, don't know why you can't. But did you press down lightly on the heatsink when you had the side cover off to see if it moved ? Because it MUST be properly installed or the processor is sure to overheat. It isn't too hard to remove and reinstall a heatsink, but if you do that you must clean off the old thermal paste from the top of the processor and the bottom of the heatsink, then put a thin smooth layer of fresh thermal paste, (preferably Arctic Silver 5) on top of the square heat transfer surface of the processor before reinstalling the heatsink.
As for your power button maybe sticking, to find the cord for it what you do is take off the side cover, then remove the front cover carefully. Some machine have clipon plastic front covers, and some have screw on plastic front covers. To see which yours is, you look inside the machine with the side cover off, and see if the are plastic clips sticking through the front metal panel on the case, or if the are round plastic legs which screws go into. Once the front cover is removed, you will see if the wires for the buttons on the plastic front panel go to buttons which are part of the plastic front panel, or if they go to buttons installed in the front metal panel which stick out through holes in the plastic front panel. In either case you should be able to trace the wires to the power switch.
But judging by the way it is shutting down this is a processor overheating problem or a Windows problem.