19.5 hp twin craftsman serial number 917259560 turn key nothing happens battery new, switch uner seat in ok position

If you were able to jump start mower then the problem lies with the battery connections or battery itself

key switch or safety switch on the clutch/brake pedal

I would try to jump the starter. Pos cable on the starter then ground out the neg, it the starter turns over that isnt it. then check the smaller wire going to your soleniod, when you turn your key to the start position it should have power. then check to see if there is power from the battery to your soleniod then with the key turned power from the soleniod to the starter.

Could be, but test each item with your tester. Test key switch (12V in and 12 V out when turned to start., operator present switch 12V in 12V out (seat) Clutch switch, etc. till finally you test for 12V on the small terminal on the starter solonoid. Happy testing!

It depends on the model but most riders have the following;
1. Seat switch
2. Brake pedal switch
3. PTO switch
4. Neutral switch (if its a shift model)

All need to be closed in order to start engine.

Check your seat, drive safety switches. Can you turn the engine with jumper cables attached to the starter? It won't start, but should turn over, one of your safety switches is not working.

lift your seat and look at the label that you got your model number from. to the right of the model number is the serial number. the first six digits of the serial number is the date your tractor was made - for example: serial no. 060802D002756 would make the unit made June 8, 2002

Those safety switches you mention above is a good first place to look. Possibly the magnetic switch that makes connection with the battery and the starter needs replaced. When you jumped the starter to turn the motor over did you have the key turned to ignition? No spark can come from a low oil shutdown switch located somewhere on the lower part of the engine (either low oil or bad switch), if the key was on. The switch can be bypassed to test its condition. Keep us posted.

Make sure there is no corrosion on the battery terminal connections and check the fuse and safety switches clutch, brake,seat.
Eric

make sure you mower deck is not still engaged. that might make it not start with that safety switch.