There are probably 3 or 4 safety switches around the tractor that you can disconnect and jump (stick a piece of wire in the 2 contacts) but the FIRST thing to check is put a multi-meter across the battery, turn on the blade switch so it'll click and see what your voltage is.
Sitting still it'll probably be 12.something if when it clicks it falls below say 11v its a dead battery, replace it before trying anything else.

I'd GUESS its the solenoid, you could probably test that theory with a jump wire from the + side of the battery. The solenoid usually (I don't know your machine exactly) has 3 connections, + in from the battery, + out to the starter and + in from the key switch. That last one will be a MUCH smaller connection, hit it with your jumper from the battery. Sometimes they get dirty and don't get the signal from the key, sometimes the solenoid is junk, sometimes the keyswitch is dirty or broken.

Most times its a bad battery, don't know why it would click with the blade switch on (seems like that would have a lockout) but I'd still bet on a bad battery, loads of times they'll fail all of a sudden, worked fine yesterday, today don't work at all.