1996 Saturn SL2 Car won't start

Car would not start - no sound or anything when I turned the key. Hooked up jumper cables and car started immediately. Took out old battery, had it tested at NAPA - dead cell. Bought and installed a new battery - car started right up thought that was the end of the problem. Third morning after car would not start again - totally dead no sound when I turned the key. Jumped it again and it started right up. Took it to first mechanic who said battery cable was loose and he recharged the battery and said it would be fine. Car started with a little hesitation and worked fine for 2 days when I tried to start it again in the morning and it just cranked but would not turn over. Took it to a 2nd mechanic who pointed out corrosion on the battery cables and cleaned them off. I also put it on a battery charger for 5 hours after which it started right up. Overnight car went dead again. No obvious power draws are there like the dome light on. Meters seem to show that the battery is low when the car won't start and the alternator is fine. I don't want to put a lot of money into this car and my knowledge of cars is poor. Any guidance would be apprieciated - thanks.