Had this happen once, it was a bad capacitor.
If you do crack it open and if there is a bad capacitor you will need a soldering iron to remove the old one and install the new one.
You should be able to tell by looking at the top of them, they should be flat, typically when a cap is about to go bad or has gone bad they will be "bulging" or "raised".
If you find a bad cap it will have the capacity and voltage rating written on it (1000uf 16V ) stores like radio shack will carry a replacement for around a $1.
Other than the power supply I don't believe there are any big caps(voltage wise) on the board.
Discharging a cap just means releasing the stored up voltage in it, the smaller voltage ones can be discharged with a small screwdriver (touching the two leads)
The larger ones I try to stay away from

but there are proper ways to discharge them.
Go for it, hell it's not working any who, just be careful!