Battery indicator light on after battery replacement

I have a 2007 F150 that sit in my garage for 7 months.  When I got home the
battery was dead so I charged it and truck stated fine but battery would not
hold a charge.  Since the battery was dated May 2013 I figured it was the
battery plus when I removed it I noticed that the negative post had started
separating from the battery housing.  Once I installed the new battery, the truck
started right up, however, the battery indicator light was on.  I drove the truck a
few miles and the light would go off then come back on periodically.  Today I
drove the truck for 25 miles and the light stayed on permanently.  I have already
cleanened the posts and terminals.  Should my next step be to have my alt
checked?  Trying to eliminate all possible causes myself before having to take
my truck into a repair shop.  Any help or suggestions will be highly appreciated!