Okay so I managed to grab a curb side discarded, somewhat recent LG 5K BTU Window unit. THe guy throwing it away simply said his wife hated the rust (not rust, dirt) in the vents after most of a summer of use.
I took it home plugged it in, and it threw the GFCI almost instantly.
IAssuming it isn't something as simple as a bad GFCI end, what else should I be looking for?