its pretty easy to tell, is it clear at a low volume and distorts when you crank it? if so you will probably need an amp, if its crappy sound at all volume levels you definatley have a problem with the wiring or headunit. if its at all volume levels the best option is to remove the headunit, get some short wires and test the speakers from the headunit itself, if its still sounding wrong, your headunit is to blame, if not that just leaves the wires. just make sure none of the wires are exposed, make sure they are all insulated properly with insulated connecectors or at least insulation tape, dont use sticky tape please!
i think thats about the limit of what i can tell ya without being there and having a look for myself. if your mounting the sub in the boot aswell make sure its in a box that matches its size, ported or unported boxes im not 100% on, i think it depends on the cone material or speaker type (anyone is more then welcome to correct me here, please) i think thats about all i can say other then test, try and good luck.
one more thing, make sure your amp&sub combo has a crossover or something in it. if you send high pitched sounds to the woofer it will be damaged, i think a lot of amps have settings built in them, just be careful, you dont want to kill your hard-earned sub!
good luck mate, hope you get around the problem soon