What to check next?

[WmWatt]

A volt meter is a good thing to have. You can check the battery voltage. If it's low the battery needs charging. You can test the alternator voltage. If it's low it isn't charging the battery.

[georgeb]

Once I drove my '93 for 40 miles at 70 MPH with the pos cable off the battery. I figured about that far because that's when the radio was acting funny. It happened because I was using a shorter battery and an insufficiently tightened pos clamp. Stuff was unharmed.