[Bob Parmenter]

Good batteries are replaced far too often by guess work. Do yourself a favor, find a reliable automotive tech who has, and knows how to properly work, a battery load tester to determine your battery condition. Then have him check the alternator, and if he knows his stuff he'll have already checked belt condition/tension.

Given your "dim-bright-dim" comment, you or he should check all the electrical system connections (including ground circuits) first.