$300 is cheap for ANY zero turn mower....
For the deck, try to loosen the belt and check idlers, spindles and belt for their condition.
The engine is the big thing... For just a bad starter, folks won't sell a $1,000 + machine for a bad $100 starter. Sooo, I would be very cautious about the engine.
W/O being able to crank it over normally limits what you can check.
Pull the spark plugs, inspect for oily deposits, excess carbon, etc.
Check the engine oil, is it filthy, low, etc
If you can, run a pretty heavy line(wire) from the positive terminal on the battery
to the starter lug. See if it spins over, just clicks, etc. If it just clicks, battery may be low or the starter bad. If it spins over, you know the starter isn't bad, there's other issues.
Look into and smell the fuel tank. If the fuel is bad, you can usually see/ smell it...
How long it's been sitting, last run, etc....
Good luck.