cooling a polyfuse does NOT help to recover it more quickly, quite the contrary in fact, normally it takes less than 48H, but if there is a short on the board, it will just re-blow.
A PI won't die from just a power cut, in that case it would be just your SD-card that got scrambled by the power loss.
However a nearby lightening strike could have damaged your PI, and that seems to have been happening.
Perhaps its just the over voltage protector diode that has given the ghost, (and now shorts out the 5V supply) its a large black device near the micro-USB port on the underside of the board, if that gets hot it has been damaged trying to protect the rest of the PI from voltages much larger than the chips can handle (>6 Volt).
IMHO you need to buy a new PI.

You will also need a new power supply as this one might be damaged as well.