What would cause the water to stop when I turn a faucet to hot?
Very small pieces of debris (very frequently rust chips in homes with older galvanized pipes) can block one side or the other of the cartridge of a shower valve.

Newer valves have replaceable cartridges than can be examined and cleaned.  Just shutoff the water, open and close the valve to relieve pressure and undo the trim plate.  

Note, examples are of Delta shower valves

The Cartridge is usually behind a finely threaded retaining nut (bonnet nut).  



Sometimes the seals break and jam..  here's a Delta cartridge and seals