I had an hp 2420 and had identical issue removing a genuine toner cartridge. Seems to be stuck on the right side (even though left side moves about 1 "). I was able to forcefully remove it to check for paper jam. But when I tried to put the toner back, it wouldn't go back all the way on the right side .
I found that on the right side, there was a white plastic circular gear lever that 'pops' out to engage the circular gear on the toner cartridge and that doesn't recess when you pull down the toner cartridge door to put in the toner cartridge (or take it out).
I figured there must be some mechanism that tells it to recess when removing and installing a toner cartridge. I traced around and almost gave up before I found out that the left side of the toner cartridge door had a half moon plastic hinged that connected to it when open. I checked the right side of the toner cartridge door and it didn't have that hinge connecting to it. I looked closer and somehow that hinge got 'disconnected' and went back into the printer body. It was easy to grab that hinged and put it back on the right side of the door. This hinge (when pulled) also recesses/disengages the plastic circular gear into the printer body so the toner can side in and out easily.
So in conclusion for a possible solution, make sure the right side hinge is connected to the toner cartridge door. Check the left side of the door to see what I'm talking about.
Hope this might help others as I was close to buying a new printer thinking this one bit the dust (after 8 years of use).