I accidentally left my client on last night, drifting in an empty sector, and when I get back to it, I can't jump, I can't get out of my trident to launch in another ship, or do anything. I was also disconnected at some point during the drift.

When I logged back on in my Trident,
1. I can't jump
2. Trident Shows no ships in hangar
3. Trident shows no turrets (in tactical menu)

Does this have to do with being absurdly far out, and how the heck do I fix this?

Yes, it does. It has happened to me twice in the trident.

You need to create a support ticket. Tell us what character is having the issue and when and we'll try to fix it asap.

Did.
Here's how to reproduce it:
Fly at least 2 million meters from the sector origin, and try to jump.

Considering I was playing, I used /explode (and was NOT happy about the fact that this is the only way out) and lost a few rare things.

I wasn't about to be waiting around for the devs to reply 2 days later, and not be able to play my character in the meantime.