I can't get a picture in my mind from your text - Hinges usually make doors open and close... yet you don't mention door at all. Drawers slide in and out on runners of some sort but yours appear to be on hinges?
To remove a hinge take out the screws - you and take the door from the hinge and then remove the hinge itself from the cabinet - or take the hinge from the cabinet and remove hinge and door in one piece.
A stuck drawer is another thing - it will be binding or be trpped by a loose article. Observation is needed to discover what it is.
Good luck...
Peccavi
August 2009