HP D4160 Ink Cartridge Cradle getting stuck

Since yesterday, my HP D4160’s cartridge cradle randomly gets stuck when in the right side of the printer. The problem is with the part in the pic and don’t know what it’s called, but the cradle can’t move from side to side when this part doesn’t move back and forth. Is this part connected with the roller, as it now won’t grab individual sheets of paper. How would I go about fixing this? The printer has been out of warranty for years, but since everything else works, I don’t want to replace it.