Another success story here. I'd previously "fixed" this TV by plugging in an IR remote sensor, but didn't realize at the time just cleaning the port would be enough. Removing the sensor and cleaning, it works.
Tip to other users: don't use WD-40 unless you don't want to use the remote plug in ever again. WD-40 does clear the fine corrosion that's causing this port to close by itself, but it can gum it up for the future. Try just clearing the problem by inserting and removing a plug a bunch of times. Or if you have to use WD-40, use the tiniest amount possible, maybe on the end of a q-tip or something.