David/Robert-
The QL tractors have a more modern bendix-drive starter and an alternator charging system, not a starter/generator. Since it is a QL, make sure that the ground cable from the battery to frame is good and is making a good connection, and also that the ground cable from frame to engine is in place and making good contact. If that all checks out I'd verify the solenoid and wiring to the starter, and then remove, disassemble, and clean the starter. You might need to replace the brushes. At any rate, I'd check out all the electrical stuff first before you pull the head or take the engine apart.
If you haven't already, download the engine service manual from Kohler's website.