My car blew a water hose and automatically shut down. now it won't start.

Not long. No more than a mile

Timing belt? some cars shut off automatically if the timing belt breaks

I actually tried jumping the starter today, and all it will do is one click. Nothing more. It almost sound like the starter is stuck.

Looks like a seized engine. Last resort is trying to get the crank to move by hand. Take out spark plugs, put a socket on crankshaft with a long extension for leverage and hope it turns.