1999 Chevy Cavalier 1999 Cavalier power problem

I'm starting to have problems losing power. It's happened to my car while I'm operating it, but only at low speeds. I've had no trouble re-starting it, however.

I've also had trouble starting it at first (from a cold start), but later it does start.

I tried to start it this evening, and the dash lights and dome lights would not come on. I came back five minutes later and it started right up.

I suspect alternator, battery or maybe even a loose connection somewhere.

Thanks in advance for the help.