1990 Geo Prizm Engine won't turn over

About every 3-4 weeks, my Geo goes through a phase where it won't turnover and start. I have put a brand new battery in, replaced the starter and alternator. It doesn't even make a noise when I try to start it. But when soemone gives me a jump, it starts? Then after about 4 or 5 jumps, it will start up fine on it's own for about 3-4 weeks and then the trouble begins all over again......

Any suggestions?????