The way you talked about the starter coming loose and there being no belt tension sounded like you were mistaking the alternator for the starter. To be sure, the starter and belts have nothing to do with each other.

It sounds like you may of/are grinding teeth off the starter or flexplate/flywheel.

If the alternator was bad then the brake and battery lights (and a few more lights depending) would be lit meaning your running off the battery instead of the alternator.

The alternator is easy to replace, I did mine last weekend.

A cam and timing adjustments would not affect the alternator.