battery? Something else?

HELP! Have a 95 Lumina 4 dr. Had cheapo battery, tested bad, replaced 4 weeks ago. Car running fine....then...it started doing what it did before we replaced the last battery....
Starts fine...most of the time. About 1/2 block later, no matter how long it sits running, it starts to act up...feels like it won't accelerate, the radio starts making freaky sounds, the led on the radio/clock flutters or goes out, and if you persist in moving...eventually, it all seems to click and work fine.

The positive connection seems a little flakey...could that be the problem or should I look elsewhere?

Flakey? Like it has a white build-up on the terminal?
If so, thats corrosion and has most likely moved down the cable..have seen some so bad it actually got inside the starter.

Electricity is like water..it flows in the path of least resistance..that corrosion is like a dam keeping the electricity from flowing.

You can clean the terminal end of your battery cable with a baking soda/ water mixture and a stiff brush (wear gloves and eye protection) although I would recommend replacing the cable.

when we replaced the battery, the corrison was BAD...there is this stupid cap that covers it...remember, this is a 95 Lumina and the washer fluid tank sits over the battery...duh...could think of better ways to do THAT!

So, we cleaned it up, and then it ran fine for 4 weeks. We had rain (unusual for August!) last week and then it started acting up again.

That's why I suspect the battery cable - the high humidity/rain seems to have helped create more corrison on that connection.

Is there anywhere else we should look at for potential problems or are the odds in our favor?

thanks! (I am experienced in auto repair....so I won't do anything stupid!)

That has GOT to be a wiring problem, which you have guessed. Something somewhere is causing resistance or grounding. If the corrosion got into those cables then replace the cables. Before doing that, track all the wires connected to the battery and the wires connected to the alternator. See where they attach (especially the negative battery cable attaching to the frame). Sometimes they get loose and cause problems. If you see no loose connections, then the cheapest thing to try first is to replace the battery cables.
If you wind up getting new cables, coat the terminals and cable heads with vaseline AFTER you connect the cables to them.. that will help keep the white crud from forming.