When I forget to connect extra power to vid cards, I usually get a long series of beeps, but it could be different for each card.
Do plug the extra power connector to the card, it needs the extra current.
Take out your CPU and using cotton buds and/or clean rag and meths, clean off every last trace of thermal compound.
When you reinstall cooler, apply just a little to CPU core, spread it as evenly as you can with the aid of an old credit card or even the nozzle of the compound dispenser, you don't need much of the stuff.
As for whether the compound can damage your CPU, some can and some will not.
Arctic Silver heat transfer compound can damage a chip as it's capacitive and can cause shorts between exposed surface mounted components.
Most other types, typically coloured white, won't do any harm.
If the cooler wasn't making good contact with the CPU, it's likely it won't POST as it will overheat rapidly, but usually this initiates a shutdown, which yours isn't doing, so that's puzzling.
Look in your BIOS and check every setting carefully, something may leap out at you as obviously wrong, it's worth looking.
Good luck.
Edit/PS: Just realised, if it ain't POST-ing, you're not going to be able to access the BIOS are you? Oops

So, er, forget that for now....