My truck didn't want to start last night, it caught then immediately fell on it's face. It did this about three times before it finally started. Then, I turned it off and it ran for about 10 seconds after I took the key out. Before I go out in the cold and replace it, just want to make sure my diagnosis is correct.

 

Have 2 people , 1 to turn the key and other to watch the linkage , see if it moves regularly .
Then disconnect the linkage , see if there is any hang up from either the linkage or the fuel solenoid .
Then look for electrical from relay / relays .
If the boot is ripped , letting the piston & cylinder get gummed up , you may be able to clean , and get a new boot .

 

If alone, get the truck started and go under the hood and try to lift the plunger by hand. If it moves up, it it sticking and needs cleaning.

 

DON'T REPLACE THE SOLENOID!!!
Likely nothing is wrong with it unless it is very visibly burned up on the outside.
The solenoid is probably the most needlessly replaced item on a 12 valve, expensive too. The solenoid is a very simple, sturdy device that will easily last the life of the truck. It either works or it doesn't, there is no such thing as one getting weak.
The problem is almost always a corroded blue wire from the driver's side battery or a bad relay on the firewall. The rubber boot that protects the solenoid can fall apart allowing gunk and rust to bind the solenoid, clean it up and replace the boot.
Relay and boot are availible for a good price here http://www.fostertruck.com/dodge/default.htm

 

Thanks for the advice infidel. I went out and took a good look and saw that the problem was actually a fuel line I had rerouted. It was so stiff in the cold temperatures it was slowing down it's movement. I just changed the angle of the fitting going into the injection pump and that fixed it.