If the battery goes dead overnight, there is a parasitic current draw. To make it go dead in a few hours, it'd have to be a fairly large draw.
Is it only the dash lights that dim or do the headlights dim also, along with the heater fan slowing down, etc? That would indicate either the alternator is failing (could be as simple as the brushes are worn out), or the regulator is failing or has a bad ground to the firewall. Also be sure the battery connections are clean and tight.
As a check for a possible cause of the parasitic draw, see if the alternator is warm or hot even after the engine cools off. If so, that is the current draw. Odd as it sounds, the alternator can also draw the battery dead if it's shorted internally and they will always be warm/hot when they do this.
If the battery runs down while driving the car, we're back to alternator or regulator or,,,,,a bad/loose connection in the circuit.
On an '89 vehicle, there aren't really any other things that could kill a GOOD battery overnight aside from leaving the headlights on.(unlike newer vehicles).
Did you have this problem before putting in the new battery? It's rare but I've seen batteries go dead overnight even when they aren't hooked up and can also cause other electrical problems like lights going bright and dim, etc..... A battery load test will come out fine and the only way to know for sure is to unhook the battery and see if it goes dead or not. I'm not sure what causes it, probably an internal short or something like that.
Just some ideas anyways.
