Diagnosis
That's the pump motor humming but the piston assembly inside isn't moving. On these, the most common culprit is that the pump was stored with water in it over winter and the piston is stuck or seized.
How to Fix It
First, relieve all pressure and disconnect the spark plug wire. Remove the four bolts holding the pump to the engine. You'll need to separate the pump from the engine crankshaft. Once it's off, you can try to manually turn the pump's input shaft with a wrench. If it's stuck, you'll need to disassemble the pump head (the part with the water inlets/outlets) to free up the pistons. Often, tapping the pistons gently with a rubber mallet after applying some penetrating oil will break them loose. Clean out any scale or debris and reassemble with pump oil.
If That Didn't Work
If the pump shaft turns freely by hand but still hums when powered, the issue is likely the unloader valve (the brass block where the pressure hose connects) being stuck in the bypass position. Remove it, disassemble it carefully, clean any debris from the small spring and plunger inside, and reassemble.
Heads Up
Never, ever run the engine for more than a few seconds with the pump humming like that. You'll burn out the motor coil in under a minute. If you can't free it manually, you're looking at a pump replacement.