John deere Z225 riding mower won't start .hour meter lights up .jumped across starter solenoid and it started three times and run.replaced with a new starter solenoid and nothing then tried jumping aross solenoid and got about a quarter turn of the motor then nothing .checked fuses and connection and safety switches and ran out of time.

This could be a starter solenoid issue. Do you do your own repairs? You can 'bypass' the solenoid but I would not recommend doing it if your not familiar with engine electrics.

Check voltage at the contactor terminals (large posts). One should read zero, the other battery voltage (approx. 12.5 VDC with engine not running).

Then check the voltage across the solenoid coil terminals (smaller wires). It should read zero, then turn key to the start position and the voltage across the solenoid coil terminals should read battery voltage. If the solenoid coil voltage does not read as batt volt when key is in start position, the problem is not the solenoid.

Check starter solonide switch

test starter and solenoid for voltage /amp draw

would not crank Chet, Relay,Solenoid or starter may be defective, give the starter a sharp bang with a hammer, to see if it is stuck.
Check the attached links,instruction and guides, Good luck
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How to Test lawn Mower Solenoids
How To Test Solenoid with Taryl
Electrical System Troubleshooting for Lawn Tractors Mowers
JOHN DEERE KAWASAKI RELAY

Have you checked battery voltage and amperage? Also check starter solenoid for 12 volts while trying to start. Starter could also be weak.

The symptoms described may indicate a bad starter. First check all connections from the battery to ground and from the battery to starter You may want to have the starter tested at Advance Auto or Auto Zone. It will need to be removed from the mower, and I am not sure if Auto Zone, Advance Auto can test small mower starters. They test the starter under load, so if you remove the starter and hook it up to a battery, it will run probably, but it will not indicate whether the starter is good or bad. It needs to be tested under load. Good luck.....

There are a number of safety switches on mowers today for example one for the seat, pto (deck being engaged) There may also be a blown fuse as you said the hour meter is not working

I need a wiring Diagram for a John Deere Z225 Mower.

Try replacing the starter solenoid. If that doesn't do it, try replacing the whole starter.