If the starter is spinning the solenoid isn't the problem, it just isn't engaging the flywheel. You probably need to remove the starter and clean and lubricate the "gear" on the starter shaft so it can engage the flywheel. At least that's what it sounds like the problem is.... something is sticky. Good luck.

__________________
1985 300D Turbo ~225k
2000 F350 (Powerstroke) 4X4, SWB, CC, SRW, 6spd ~148k
1999 International 4900, DT466e (250hp/660 ft/lbs), Allison MD3060 ~73k