Today, when turning the water on to fill my sink, I hear a 'thump" and the water is shut off instantly - the hot AND the cold water! Reading a previous question and answer, it was suggested the strainer might be plugged with calcium. That is not the issue with my faucet, as I have actually used it without the aerator!! BUT, it hit me that maybe there is a bit plastic from the lift tube, in the water heater, that had disintegrated a number of years ago, might be causing the problem! Could that be??
Start by shutting off the water supply for the Hot and Cold lines under the sink.
Next detach (unscrew) the hot supply line from the faucet line (if possible). If you can't than unscrew the hose from the valve.
Place a bucket under the valve and a rag over the open connection. Slowly open the valve to check for water flow. When (and if) water is flowing into the bucket open the valve more to jettison any debris in the line. Do the same for other side.
If no water is present at the valve than the problem is before the valve. When you reconnect the faucet hose after confirming water is flowing but no water flows from the faucet thr problem is after the valve.