IIRC, if the key is in the 'R' position and not OFF, this port should be live. Sounds like you've thoroughly tested that though. The next step is to ensure that the fuse is not blown. The easiest way to check this is to see if the light is working inside the top case. If it comes on, then the fuse is obviously OK. (If your LT is a pre-'05, we're talking about fuse #8 here. Bottom fuse in the middle fuse block.) Of course, if the light does work in the top case, we're looking at a few more possibilities.
A bent pin in the electrical barrel-connector of the top-case. HIGHLY unlikely.
A broken wire to the Powerlet port. Not very likely.
Corrosion inside the Powerlet port. A better possibility.
Ensure the device that you're using to test the port works properly.
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