I've got a 88 DL sedan, its battery (which was 2-3 years old) seemed to have died, so I had the battery recharged. It worked for a couple days, then the car had no response at all thereafter. No lights would work, wouldn't attempt to turn over (or even "click" when I tried to start the car), nada. So I replaced the battery, and it worked for a few days. However, now it's not doing anything at all again. What gives?

alternator?

 

I have seen new batteries that are BAD out of the stores. But not usually 2 in a row.

 

So yeah, alternator.

You should be able test the alternator by measuring across the battery terminals with a multimeter (fairly cheap at radioshack or you can get a better one from an electronics supplier.) When the engine is running the terminals should read 13-14v. Or you usually get a place like sears parts or another place that sells batteries to test it for you for free. I had to replace the alternator in my forester a few years ago when the battery kept dying. If it is the alternator do some research on here, there may be a swap from another car that will be an upgrade to support future accessories if you want to add more lights or whatever.

Now way to check voltages, but unhook the battery when the car is running, if it dies the alternator isn't working.