1998 Honda Civic Ex ignition problem!?

One day I left my car radio on without the car running so it ended up killing my battery. I jumped it of a few minutes later, it started fine. The next day I was driving it and i got out and about 10 minutes later got in and tried to start it, and nothing happened. The engine didn't turn over, but all of my lights and everything worked. I jumped it off and it started easy, I went to O'reilys, they tested my Alternator, and my battery. They were both good. I put a new starter in it, and it didnt fix it. Please help!!