I just purchased a used 1986 John Deere 310B and the only way I can get it to both, stay running and have any kind of power is to remove the governor screw on top of injection pump, when I do remove the screw it runs great. I removed the little side cover on the pump and I didn't see any type of trash and it looked clean. I also removed fuel return line and blew it back to tank with air and then re installed it.
Also the oil is a little over full and seems to have a little diesel fuel in it.
Possibly the problems are unrelated. Take the adapter FITTING off of the injection pump that the return line is attached to, if that's a check valve that is plugged up, blow it clean, reinstall, and try it again. If it runs, that's a temporary fix, and the engine may run away at some point. Post a pic of the junk you find too.
Delmer is spot on with his suggestion. The case pressure valve has a glass ball in it and if the internal drive dampener ring is starting to come apart, it will plug this valve and it will start, run for a short time and die or run with no power. Remove it and see if it improves any. If so, you can run without it, but be mindful of engine speed as the dampener failing can eventually lead to a runaway.
Fuel in the basement will most likely be from leaking injection pump shaft seals, or a ruptured diaphragm in the transfer pump.