Toyota - Camrysolara :: 2008 - Engine Won't Start?

I have a starting problem that is a new one to me. After leaving my car at the airport for two days, when I returned the instrument lights lit up but engine would not turn over. I had it washed too, so I figured the guys left a light on...nope. So I turned the ignition switch off a waited a bit, and the engine made 1/2 a turn. I waited a bit more, then a full turn. Long story short, after enough of these cycles, the engine started and I drove home, no problem. The next morning, I figure the battery is well charged, but I get the same behavior. I've had many experiences with batteries getting progressively weaker as I try to start, but this is the first time I seen a battery (or at least starter) get stronger with start attempts. The battery is well within its warrantee period, but this is Texas, so maybe it's dying already. But I don't want to go drop $120 if there's something else to look at first.