The non booting issue occurred after you changed the case, or after you changed the fan?
It sounds like you would have caused a problem if that's the case; seeing as the problem became apparent after modifying the computer.
If your motherboard has an integrated GPU, try booting off of that. Also, try re-seating your CPU and making sure than fresh, new thermal paste is on the heat-spreader. You only need a tiny amount for it to spread thin, thick is bad and can cause issues.
Another possible issue would be your PSU not delivering the required power at start-up. Even though it's a Corsair, it seems to be the lower end (CX iirc) and could be faulty.
Edit: If the CPU has overheated multiple times, it may have been damaged. Most of the time they shut down and blue screen before going over their limit, but not always.
Try disassembling the computer, make sure that nothing on the motherboard is grounding out.