1) Charge the battery. Verify it actually takes a charge and is ok.
2) Next, presuming it starts, take a voltage reading at the battery with all electrical accessories off @ 2000 RPMs. Expect about 13.5 volts.
If it still does not start, it may be a fuel problem. The battery problem may just be a distraction, since the attempted restarts are taxing a marginal battery more than normal use would. [That is exactly what happened to me when my fuel pump failed!]
3) Turn on rear defog, fan on high, and lights on highbeams.
Expect at least 12.5v @2000 rpms.
If tests 2 or 3 fail, replace the regulator and try again.
If still no good, replace (or rebuild) alternator.
[Some folks swear a DIY rebuild is easy, and usually it's just the brushes or the bearing that has gone bad, but I have not tried this myself]
Best rebuilt deal I know of:
This was cheaper than most used quotes, plus a 3 year warranty. You will even get a little rebate back for the core after return shipping charges ($13 shipping for me, $25 core).