Easy alternator test :
If you don't have a voltmeter/multimeter, go get a cheap one from Radio Shack or WallyWorld. ( you can also get a digital voltage meter that plugs in the lighter socket from most any auto parts store ) or :
http://www.ebay.com/itm/LED-Display-...ht_3533wt_1397

I just ordered 4 of those, total was $10.86

1. Measure between battery terminals with car off : should be 12.0 - 12.7 volts.
2. Start it up, should now be around 14.7 Volts.

if 1. not OK - then charge the battery and try again.
if 2. not OK, then alternator issues.