1999 Ford Escort Dim headlights/dashboard; new battery

Okay, my battery light turned on 2 days ago. I got it checked out and they told me my battery was dead and so was the alternator. I got both brand new parts installed. They also had to install a new wire that connects to the terminal (I believe)

When my check-battery light came on, both my headlights and dashboard lights dimmed to about half brightness. So I got the car checked and fixed the next day.
The night after my car was serviced, when I turned my headlights on, both the headlights and dashboard lights were at full brightness for about 10 minutes, then they dimmed back down to how bright they were when my check-battery light came on. The battery light is not on now.

During a 2 hour drive, they did get bright again. But for only about a minute. Then they went back to half brightness.

I got my car serviced at Pep Boys (if that helps with anything.) And the service sucked, it took them from 8 am until noon to diagnose the issue, then noon to 1 to install the new parts.

Did they screw something up? Could there be a loose wire? Or did the battery dying damage something because of a drop in voltage?

Thanks