2000 Toyota Solara starter issues

[tpjv]

I have a 2000 Toyota Solara that recently has had some issues starting. The first time was one day at home it just wouldn't start. I had just started it about 30 minutes prior, but when I tried to move it, I got nothing. Putting my hand on the starter, I could feel it trying to start the engine, but there was no clicking to indicate that it was turning over. I replaced the starter and the car started normally. It started a total of three times (the test to see if I fixed it, once leaving for work, and once stopping for breakfast on the way to work) before it wouldn't start again. Same symptoms where the starter feels like it's trying to work but won't turn and again, no clicking noise. I tested the battery when I replaced the starter and it was putting out the normal 12.5 amps that it should, plus I've tried jumping it both times just to make sure there wasn't a draw somewhere that keeping it from working. Is there something else I'm missing, or could this just be a consequence of getting a refurbished starter that was a lemon? Any insight would be helpful.

Thanks.