1990 Mazda RX7 Engine won't start

My problem is a bit of a two-parter. The main problem with my car is that it won't start. It's been having trouble turning over and catching, then staying on. I almost had it going when I let off the gas and it died on me. Since then, it seems my battery hasn't been able to keep a charge, even after being hooked up to a charger for half a day. I have since changed batteries, and blown my fuse with the new battery. My question is this. Do I have a lengthy, expensive problem with my car. I know that I need to get a new fuse, the main one, and I need to hook up my new battery. But after that, I'm not sure the problem of my car not starting will be resolved. It's been having trouble starting in the past. When I turn the key, sometimes it just makes a clicking noise without the engine turning over at all. After 3 or 4 turns of the key, it finally starts, but very softly. It also billows out quite a bit of white smoke, which makes me think that there is something either wrong my catalytic converter, my fuel filter, or something to do with my radiator as I've been having trouble with that lately. I have yet to buy a new fuse, I'm just curious as to what else I can do before taking it to a mechanic for a lengthy repair and stay.