Hi;
You certainly can desolder the cap with a just a soldering iron and a solder wick if you want to.
The cap is the same as the rest of the other tantalum caps on the board - 100uf, 16volt 20% tantalum capacitor.
But before you continue;
If all the fuses are verified to be OK then,
If the cap is shorted, then there will be no sign of life as you said.
otherwise, if the cap is open, it should show some sign of life.
So, with that said, use a multimeter to measure ohms across it to see if its shorted or not.
If it is not shorted, then I am afraid this repair is not worth your time.
If it is shorted, maybe, just maybe a simple replacement of the tantalum may be worth the risk and your time.
HOpe it helps.