No cold water in kitchen taps

Is there a separate isolating vale on the cold feed to your tap that has been turned off or has the vale in the tap broke which enables to feel like its opening and closing but not doing anything at all.

Did you turn the stop cock off before you left to care for your mother? Or any other valves before you left? What system do you have for hotwater? if you have a cylinder for hotwater and tanks in the loft. It could be that you are getting hotwater and cold in the bathroom because they are still being fed by the tank in the loft. While the kitchen sink tap which is usually fed by the mains as it rises to the loft is not working because the mains is not open. Do you have any other cold water taps connectd in the kitchen eg washing machine outide tap are they working? Is the mains coming into the house turned on or off?

Cold tap probably stuck in closed position, needs tap taking apart not much of a job for a good plumber.

Tap valve turning but not letting water through. Need a new insert

Depending what type of plumbing system you have if it is a gravity fed system you could have an airlock. This would need to be pushed out off the statements then water should flow again.
Could be a faulty tap you ring turning the tap but it is not opening inside. There could also be an isolation valve that has been turned off

Possible kitchen cold pipe freeze

Faulty tap

Possibly needs the cold cartridge replacing.

Maybe cold side feed to tap is scaled up or not opening. You need to turn off Isolator and disconnect cold feed to tap then turn on Cold Isolator and if water comes out then you know the tap needs changing or repairing