first off it sounds like there is some good advice here. Definatley improve your ground connection, its important this is good (I always tied into a bolt that attached to the frame). if your amp is not turning on, with a proper circuit (test it with a test light to make sure the power is live and the ground is grounded), check your remote. Make sure that the connections on your remote are good and that you are tied in to a switch power supply (if you cannot properly tie into the stock radio power supply, try tapping into something like the power windows (if you have em) or the ignition itself. Just be cautious not to hard wire it (constantly on), its easy to drain the life out of your battery if this is the case.
Now, if the amp is turning on, but you are getting no sound make sure the sub is wired properly, are you bridging the amp, did you do it right? Also, figure out what your ohm load is (sub, dual voice coils? and wired in parralel or series), make sure your amp can handle the ohm load. Also, remember that you only need about 1/3 of the rms of the sub to make it work, but if you are wired up wrong (like dual 8 ohm coils wired to 16 ohms) your amp is most likely putting out very little power.
The idea of a cap also came up. General rule of thumb used to be 1.0 farad per 1000 watts, however you don't really need it unless your alternator is crap. All a cap is going to do is try to add a little bit of juice to the power that the amp is drawing (so as to try not to force the alt to work harder). However at 300 watts, I highly doubt there really is a need for a cap (but there might be depending on how much bass there is).
life is too short to have any regrets
