I have a JD 4600 and have had problems with the fuel shutoff solenoid. Looking at the exploded diagram for the 2210, it looks like a very similar solenoid, possibly even the same one. In my case it was the infamous thermistor that failed, so initially I would have an intermittent start and eventually I couldn't get it going at all. With the 4600, the fuel solenoid is spring loaded so it is normally extended, then when energized, it retracts. So in my case, I could simply remove the solenoid and it started right up. The problem was, with no solenoid in there, there was no way to shut the tractor off. So temporarily, I could reach in there with a finger and press the tab that the solenoid pushed on to shut it down. With the solenoid out, I always get a small drip of oil leaking out of the opening while the engine is running. That solenoid is fairly inexpensive on ebay, so in my case, I hacked into it and removed the spring. Then I attached a small pushrod to the end of the shaft with an epoxy seal so I could push it in by hand whenever I want to shut down the engine. I actually ran the tractor like this for several weeks until I figured out that it was the thermister causing the problem. I eventually replaced the thermister with a pushbutton switch and it has run great now for a couple years. I have a thread here on tractorbynet where I described that in detail.
With all that said, if it's easy to pop your solenoid out - it should be held in by two bolts - then do so, and if the engine runs fine, you've at least isolated it to being related to the solenoid.
With all that said, if it's easy to pop your solenoid out - it should be held in by two bolts - then do so, and if the engine runs fine, you've at least isolated it to being related to the solenoid.