I have a Inspiron 6000.  My battery hasn't held much of a charge for the last 6 months or so, but it always worked fine if it was plugged in.  It was working fine last night, but when I went to use it this morning it was dead and the AC adapter (65W OEM) light was out.  If I unplug the adapter from my computer and the wall, then plug it back into the wall, the green light comes back on.  But as soon as I plug it into my computer the adapter shuts off and the green light goes away.  I've tried multiple adapters and tried other Dells on the same adapters and everything else works except my computer.  I've tried plugging it in without the battery in, still no luck.

What's going on and where do I get it fixed?