I first had the same electrical gremlin as jonnyc1999 as as result of the tin battery cable connectors, but now my problem is quite a bit more difficult.  Dashboard lights come on, and I can hear the click at the relay when I sit down on the seat and trigger that safety mechanism.  However, there is nothing come from the starter.  I could still jump the tractor at the starter solenoid, so I replaced the starter solenoid--didn't fix the problem.  I replaced the relay switch--no fix.  I replaced the ignition switch itself--no fix.  I replaced the battery--no fix.  The PTO is not engaged.  I have checked the safety switch in the seat.  I have moved the tractor in out of gear and rocked the hydrostatic forward and and reverse pedal.  Anybody have any suggestions?