Is it a V10 ? We had that happen and there are two (2) solenoids. One not even in any of the diagrams. One by the starter - the other on the passenger side behind the front tire. Very hard to reach. We tried from the dog house first, DH arms were not long enough. Was able to reach by cranking the front wheels to the left and reaching in behind the tire. We had been having problems off & on with it starting sometimes after a 3rd/4th/5th try, just a click as you describe. Had replaced the battery, starter, starter solenoid and ran across someone else's post that told about the 2nd one. Went to leave the campground and it wouldn't start. DH was going to try to reach it - couldn't - tunked the area with a wrench and we got it to start. Went on to our destination (summer job) and didn't shut it off in between. Replaced that solenoid and no problem for 3 years now.