DIAGNOSIS Mineral scale or debris has seized the valve stem, or the plastic has deformed from pressure or temperature.
FIX Shut off water supply upstream first. Gently try to turn the valve with a pair of pliers, gripping the blue knob firmly but without crushing it. If it moves, work it open and closed several times to free it. If stuck solid, you'll need to replace the entire valve assembly, which may require a new filter head.
IF THAT DIDN'T WORK As a temporary measure, you can bypass the whole system by connecting the incoming water line directly to the faucet line using a 1/4" compression coupling.
HEADS UP Forcing the valve can shear the stem, causing a sudden full-bore leak. Have towels ready and know where your main shut-off is before attempting.