My mtd riding lawn mower stopped working while I was cutting the lawn. No power when I turn on the ignition but the battery is fully charged. It was like a wire broke but I find no cut wires. How do I check safety switches? Or how do I check solenoids?

Check wires at ignition switch

Check wires in switch as mhandy mentioned

If that gets you no where then do this next..

The safety switch that usually a pain is under the seat to sense there is a rider to operate the mower. It's a grounding wire to frame/seat

To test the solenoid use a screwdriver to jump the hot post to activate starter.
Or
YouTube - How to test a Starter Solenoid (http://www.youtube.com/watch?v=EQJPKO53FTg)

http://www.cruisersforum.com/forums/attachment.php?attachmentid=2616&d=1202377668

I doubt it's a solenoid because it won't shut the engine off that way. It's an ignition coil or a safety switch that would normally due it. Check for rust under seat for grounding for seat safety switch.

You can jump a safety switch with a wire to test the safety switch theory.