I thought I had the same problem with mine when I tested voltage. Got full voltage to the starter when I turned the key. So I have a Snap-On pushbutton starter switch, it has heavy cables with alligator clips on the ends. You hook one end up the battery, and the other to the solenoid, put the key in the run position and push the button. It's great for checking starter issues. Well, here I thought it was the starter solenoid, and it's turned out to be the relay after all. I hit the button and it cranks right over.
When you look at the firewall from the front of the tractor, there are three relays on the left side above the gas tank. The starter relay is the one on the left. The one in the middle is the glow plug relay, and the one on the right is the stop relay. I picked up replacements for all three from the dealer, they are pretty cheap, but usually I just tap on the relays when I have an issue and it fires right up.
The one time it didn't, it turned out one of the main fuses was blown for some reason, they are electrical taped to the wiring harness by the starter.