Jumper a wire from the small wire to the big positive cable on the starter. Disconnect the lead coming to the small connection first. If the starter operates, then you probably have a fuse blown or a bad switch. If the starter does not operate, then you have dirty battery terminals, bad cable, or bad ground connection. Sometimes low power circuits can work, but the starting load will cause dirty cables to open. To me, your problem sure sounds like a fuse, but all this is a guess without hands-on.