One problem related to starter solenoid has been reported for the 2004 Ford F-250. The most recently reported issues are listed below.
In 2004 I purchased this vehicle brand new. Subsequent expenses to maintain this vehicle in working condition have been extensive. 11/16/05- fuel injector wiring repair, exhaust pressure replacement, air cooler duct replacement (warranty) 11/1/06 - water in fuel light, throttle unexplained acceleration. 1/8/07- runaway throttle stalling, hesitation. 10/31/07- stalling, hesitation replaced main wire harness. Replaced elbow on turbo. 12/5/08- egr cooler failed, turbo had water and rust, replaced same. 10/15/09- replaced starter ficm module. 1/15/10 replaced ipr valve & vgt solenoid, egr cooler failed again. 6/8/10- diesel head stud parts for repair. 6/24/10 - regulatory & kit, gasket-cylinder. 7/7/10- head stud modify. 7/20/10- replaced high pressure oil pump & power steering pump. I have spent $15,135. 17 more for repairs that seem to be repetitive and very expensive. Based on the repair record I think that even you would say that there is something very wrong with this vehicle's engine. I have had this truck for eight years and have finally contacted Ford motor company only to learn that they are unable to assist with the cost of any repairs beyond the normal warranty provisions.