I have a BX2350 in about the same condition. About 900 hours when I bought it, every panel and every light broken, everything that says "do not step" has been stepped on and ruined.
I bought it cheap, and it runs great. Never had a mechanical issue, it was just that the panels were weak and got damaged (and they probably let the apprentice drive it).
Tests I can think off:
- Look at the fan
- stand on the brakes and on the go pedal. In high it should be able to stall out the motor I believe, otherwise HST is slipping. In low if it should spin the wheels if it's hitched to an immovable object
- my mower deck had been pretty abused, needed a few things welded up. Dealer should do that for you if you notice them, so worth looking under the deck and around it for cracks etc