What's wrong with my derailleur?

many things could be wrong. The housing could have come out of the end stop, or split in some way. The inner cable could have broken. The pinch bolt that clamps the cable could have been too loose. the shifter internals could be messed up.

I can only guess.

Twenty to one something is binding the cable. It isn't rare for mud or dirt to get into the short housing length from the chainstay to the RD, or one of the other short sections. If the bike has been idle for a while and has a steel noodle, it might have rusted enough to bind the wire. Since the lever can only pull the cable and not push it a sticky cable acts exactly as you describe. The second possiblilty is that the return spring on the RD broke or got dislodged.

Either way, once you pull the RD to the low gear position, it's there for the duration.

Diagnose/clear it by pedaling and pulling the derailleur outwards at the same time to get it back to the outer (high gear) cog. Check the spring by pushing it in slightly and seeing if it springs back, if it does start checking the cable section by section. Odds are you'll have to disassemble the cable and flush out each section of housing. Good luck.

I'd check the cable. It's probably broken somewhere.
Check if the cable moves at the derailleur when you shift. If it doesn't, then it's broken.