sometimes the awnser is more difficult. Repairing the Super Nintendo i encountered several problems of which bad capacitors and a corroded reset switch are most common.
The caps used in the 90's aren't the best ever. Since you can't look underneath them you need to 'wiggle' the cap to see if it is loose. If so the legs could be corroded. but, there are only a fev capacitors on the board so i say repace em all for a buck or 3 to be sure.
Second is the reset switch. Normally when you press it you short out two contacts. When the switch is corroded or broken, the swicht makes contact all the time and therefor it cant start because it is resetting all the time.
There are several other options but these are fairly easy to check.