John Deere 410C Backhoe. I had a problem last winter, it'd die driving down the road. Figured out a check ball in the return line from injector pump to the tank was getting blocked. The Pump Guy SC explained the problem. A friend, along with my son grabbed the ball & ran with it. A local guy rebuilds your pump at your location. He tried in bitter outdoor cold, but broke a screw backing it off. He returned with the pump rebuilt a few days later. It now starts well, runs fine, plenty of power, but don't shut it off warm engine, it won't restart. A few revolutions of the engine, it sounds like it's going to fire, then starter goes sluggish. I think battery. Cables are all new, contact points polished & greased with Noalox. Batteries test good under load test. Injector timing. Do I need a lift pump?
Mine had a very similar problem for a while and it ended up being a bad electrical connection feeding the fuel shutoff solenoid on the injection pump.
Try the old school trick of turning the steering wheel while cranking it hot.
Fuel tank vent?
I'll check out those suggestions. It eventually starts but I feel it should fire right off once warm.
My old 310 with the little 3 cyl will crank over slowly in a hot restart, I just turn steering wheel while cranking the engine to unload the hydraulic pump, works every time.
Does the hydraulic pump have a manual destroke screw ? If it does try screwing it in and see if the cranking speed changes.