1994 Grand Prix Giving me a hard time starting

So, about 2 months ago my car would start up right away. Some times it does nothing- no clicks, cranks, nothing. Other times it will try to turn over but doesn't. During this time my lights, radio, windows all work. I had the battery tested and it was fine. I took it for an oil change and had the mechanic look at the starter and alternator. Both were fine, but he said I needed a new battery. Bought a battery at Wal-Mart and my boyfriend put it in. Still did the same thing. Oh, I forgot one thing. Some times if it doesn't start up right away (especially if I try to start it up soon after I first turn it off) I have to let it sit for anywhere from 15 mins to an hour before it starts up again.
Now- 2 years ago, my key broke off in the ignition- 1/2 in the cylinder, 1/2 on my keychair. I rode around like that for 2 years. Thought maybe that had something to do with my problems- so I had the ignition cylinder replaced and 2 new keys made. It was fine for 2 days, and this morning it started right up- drove 40 mins, got coffee and when I came out it wouldn't start up. 2 hours later it started right up.
the mechanic that replaced the ignition cylinder told me at the time I needed new battery- they charged it up, but again- my lights, radio and window work. Could i have gotten a faulty battery that's not holding a charge? THey also mentioned a belt tensioner but didn't think i needed to do that right away. Could this be the problem too?
Any advice would really help!! I don't want to keep bringing it to the mechanic...