Ok, odds are slim, but it could still be the battery. I'm going to vote for a bad connection somewhere- possibly a ground, but maybe not. I would test the battery with a load tester- do a few times allowing the battery and tester to cool between tests. I've run into problems like this on customer cars and they'll tell you everything under the hood has been checked and/or is new. Then when the problem is located you get "....but I just replaced that and it's good, I checked it." Re-check EVERYTHING you've already checked and recheck it all during one session so you don't skip or miss anything.
You need to carry with you a test light, a volt/ohm meter and a jumper pack until you find the problem.
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