1999 Volkswagen Beetle Alternator?

I drove my car to work this morning with no problems and drove it to lunch this afternoon with no problems, and then tried to start it after a 45 minute lunch and it wouldn't start. The battery was dead. I was able to get a jump in order to get back to work and then the car wouldn't start again after I got off work. I got a jump and drove straight to my local PepBoys to get the battery replaced (it was still under warranty). After waiting at least an hour, I tried to leave with my new battery installed and suddenly the battery light icon was on and my headlights were flickering--something the repair tech didn't mention after he cleared me to leave. I went back inside and they tested the new battery, which was fine and told me it was my alternator and that I should come back tomorrow to get that replaced for $400. The car drove home the 2 mile distance or so just fine with the battery icon on the entire time (although the headlights did stop flickering).

I understand that the problem with my car is symptomatic of an alternator issue, but before I take it in to get the replacement, is it at all possible that the battery was improperly installed causing a connection problem with the alternator? Is there anyway for me to look into that myself before taking the car into the shop?