Does it click or anything? Sounds like a bad solenoid on the starter or a short in the wire between there and the key to me. If you could get to the starter you could use a screwdriver or something to bypass the solenoid and kick the starter over.... but I doubt you can get in there (be careful when trying this, make sure you're in park). Hopefully someone else will have a better idea. Double check the connections around the starter too.

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