I'm assuming you are referring to a processor, not graphics card.....with the former there's usually a thermal cutout to prevent damage.
When you replaced the heat sink did you use thermal paste and refit correctly? Just a small amount is required, literally a couple of strips a milimeter or so wide, then place the heatsink ontop, tighten on the diagonals so it's flat on the CPU.
Possibly something is loose - Disconnect from the mains before you do any work at all on the inside - check the CPU and heatsink are properly seated, the heatsink fan has power, and everything like mobo, RAM, CD/DVD any other item is secure in it's slot, that wires are connected,
Now reconnect power and try booting up.