Similar problem, also in a crash, but the problem was happening before the crash, and now after I get it back from the collision shop. It seems to work for two weeks every time another mechanic gets a hold of the thing.
Before I took it to the shop I tried the usual. Replaced the starter with a rebuilt. No joy. Replaced the relay. No joy. Replaced the battery (turned out to be bad), no joy. The tow guy came out to tow it, and tried to start it first. He wacked the starter solenoid good and it started. Started like that for a few weeks, then same problem.
Original shop (pre-crash) said it's the rebuilt starter, though they said they cleaned leaked oil off the starter and got it to work. Collision shop had a similar problem. It was working great up until about the last day they had it. The started the truck to move it, then a few hours later tried to start it again but all they got was the relay click. They replaced the starter, and it worked great for two weeks. Now all I get is click again.
So I know I have a good battery, the engine is fine, the starter relay is fine, the battery is fine. I know it ran for a while after each shop had it. I had the auto shop guy bench test the starter before I took it to the collision shop, and it worked great.
I think I'm down to a bad wire somewhere. It seems like a problem with the ignition switch or the clutch switch would mean no relay clicking. Is that right? The relay clicks every time. Nice loud click. Just no rr-rr-rr.
I did my novice version of a voltage drop test and did see voltage going around the starter wire (thick wire from fender relay to starter post.) I'm assuming that means it's a tired old wire. Any other suggestions?