Had a similar problem with my 755 once back in the summer. I had to remove some of the wiring harness to change the glow plugs and disconnected the shutdown solenoid. When I put everything back together the tractor would start up run for a couple seconds and then shutdown.
The shutdown solenoid has two important wires, one pulls the slug into the coil and the other holds it. The first one is connected to the starter solenoid to give the coil a little more kick to get the slug moving, the the second is connected to switched side of your ignition switch, kill the main switch and the slug is released and the engine shuts down.
The solenoid is located on the side of the injection pump (at least on my 755) and when you turn the key on it should do nothing, hit the starter and it will pull back. After you release the key it should continue to hold, if it releases you're close to finding the problem.
The next thing I'd do is use a battery charge or some other 12V power source and bench test the solenoid and see if it's latching or not. If the solenoid tests ok there is a relay on my 755 that controls all of this stuff, I would assume yours is similar, take a look here and see if you can see anything.
Hope that helps you a bit,
Jason