Starter problem?

[Atommik]

1951 Chev, S10 swap, 327, auto trans. I thought I was having alternator trouble based on a test at the local parts store. Turned out my alternator had gotten a little loose so the belt was slipping and the battery wasn't charging correctly. Easy fix. Took a nice long drive, shut it off, tried to start it and it would not turn over. Jumped it and it started right away. I had the battery tested(it's only 3 years old) it was fine. I tested the alternator with a volt meter, putting out 14.8 at the back of the alt (single wire). Voltage at battery while running is 14.6. The voltage at the battery with the truck turned of reads 12.8. Shouldn't that be enough to turn it over? Is it possible that the starter solenoid is bad? Or maybe a bad connection at the solenoid? Would the extra 1-1.5 volts from jumping it make a difference? I thought if the starter/solenoid was bad, it wouldn't start even with a jump.