Tractor clicks when key is turned, but doesn't always start.

If you have a new battery and it clicks, it is not a safety switch, but we won't rule out the solenoid yet, I would say dirt, check the battery terminal for dirt, clean them up with a wire brush, Make sure the battery is good, test it for voltage and specific gravity, one of those floaty ball things. Try it, if it still clicks, get the hammer, tap on one of the bolts holding the starter, just lightly to loosen the solenoid, if it jumps to life, you have found your problem, if not, Hit it harder, no, It doesn't have to be hit hard at all, just a tap will do it. My John Deere tractor has a hammer on the running board, the only way I can start it. The bolt head is rounded right off. Been like that for 15 years. Hope this helps.