Single and two handled faucets are different in the exact mechanism but the overall process is the same. Inside of the faucet there is a valve that diverts water from the main spout to the sprayer. Squeezing the sprayer handle opens its valve, releases pressure in the faucet, and diverts water to the sprayer.
It sounds like this internal valve is jammed or broken.
Call the manufacturer. I had this problem in the kitchen and Moen (the maker) provided directions on how to fix it. They can also direct you to a source for the parts.
Visit a Plumbing supply store. If you go during the less busy times of the day (late morning before lunch for example) they will often take the time to work with you.
Replace the faucet.
Possibly unscrew your aerator at the end of the spout and see if the screen is clogged. Blow it out and rescrew the aerator on. If that isn't the problem, sometimes things get caught in the spout. Unscrew the spout and turn the water on. If there is water coming from there and not out the spout when it is hooked up, the spout is plugged. If no water coming out when the spout is off, rehook spout and change cartridges or stems in the faucet AFTER shutting the water off. Depends on the brand of faucet, check the instructions for the brand and model. Also your kitchen dishwasher and sinks are run on seperate valves. The dishwasher valve is usually under the sinks (causing the water to go to the dishwasher first) the valve that was installed for the sink (before the dishwasher) may be bad too.
The screen in the end of the spout is probably clogged.
To drain the water that is in the pipe or spout..
To replace the screen on your Moen kitchen faucet, first turn off the water supply. Then, unscrew the aerator from the faucet spout using pliers or a wrench. Remove the old screen and replace it with a new one. Finally, reattach the aerator to the faucet spout and turn the water supply back on.
Turn off the water supply to the faucet. Unscrew the aerator from the end of the faucet spout. Clean the threads on the faucet spout. Wrap new plumber's tape around the threads of the new aerator. Screw the new aerator onto the faucet spout. Turn on the water supply and check for leaks.
An aerator is on the end of your kitchen or bathroom faucet spout that unscrews and holds the screen and/or water saver.
it blocks the water from coming out of the spout & redirects it to a different exit point
To replace the aerator on your Moen kitchen faucet, first, unscrew the existing aerator counterclockwise using pliers or a wrench. Then, clean the threads on the faucet spout. Next, apply plumber's tape to the new aerator and screw it onto the faucet spout clockwise until it is securely in place. Test the water flow to ensure the aerator is working properly.
The shut off valve under the sink, the faucet itself, or most likely, the screen in the end of the spout is plugged. If neither hot or cold is coming out, it is kind of unlikely both shut off valves and both sides of the faucet would go bad at the same time. The screen being clogged would stop any water from coming out. The screen just unscrews out of the spout.
Employ a plumber.
To perform a bathroom faucet aerator replacement, first, turn off the water supply to the faucet. Unscrew the existing aerator from the faucet spout using pliers or a wrench. Clean the threads on the faucet spout and the new aerator. Screw the new aerator onto the faucet spout in a clockwise direction. Turn on the water supply and check for any leaks.
A copper kitchen faucet offers more fresh water compared to the stainless steel faucet. The copper kitchen faucet also has more powerful water energy and valves.