Husqvarna Will Not Start

I have a 54" zero turn Husqvarna with 26hp Kohler motor. Installed new battery yesterday and started mower. Clicked a few times when trying to start, but after bumping the key, it started and ran fine. Only cut for about 1/2 hour because it was late, but when I parked it, every time I got up from the seat, the mower wanted to cut off. Parking brake was on, it was in neutral, and blades were disengaged. Today I went out to cut grass, mower turns over, fires, but shuts off the second I let go of the key and it releases the starter. The brake safety switch and seat safety switch appear to be working fine after testing with a meter. The mower will not turn over if either of the drive levers are out of the neutral position, so I am assuming that the neutral switches are working correctly. Cranks and fires every time the key is turned to start, but shuts off the second the key returns to the run position. Any help in figuring this out would be much appreciated.

Check out the key switch, or replace it. that's where I would start....

You have a wiring fault.
Now there are 2 ways to approach it.
1) check & / or replace parts at random based upon the symptoms
or
2) use the wiring diagram to locate the fault .

Some times you get lucky and No 1 works first up.
However most times all that happens is the parts shop owner makes a lot of money.

Now to go the second way we need to know the model number & serial number from the tag which is usually under the seat.
ZTR's tend to have relays controlled by switches where as tractors just use switches mostly.