I recently went to show with my '37. I drove 60 miles in 90 degree weather to get there without any problems. I shut the truck off and wandered around a couple of hours. It was way to hot to stay so I jumped in and hit the key, nothing, just a click from the starter solenoid. I had trouble a month back with the starter, and after pulling it apart and putting it back on, the truck fired right up. Fast forward to the show, I again pull the starter apart in the show field, put it back together and still nothing. By now I am really hot, mad, and dirty so I go cool off, clean up, and get so tasty popcorn. 40 minutes later I am back at the truck, decide to slide under and check the battery. Both cables bolts are tight, but the ground side cable moved a bit. Turned out the (side post) bolt bottomed out before the cable got really tight and over time it loosed up. With a washer added, the truck fired right up and has run great ever since. The battery has been in the truck for 5 years, it took it that long to fail. It was the first time in 15 years that I had to work on the truck to get back home!
Check your battery connections!