I too have just suffered this issue oddly enough, though my car doesn't have a fob, just central locking.
It suddenly stopped working, the interior dome light wont go off (unless set to off) and the beeper for the headlights being on with a door open no longer works.
Been reading the Haynes and found that all of these things go to a box under the drivers dash, right in the middle pretty high up. You can see it from the footwell if you get in there and have a look up there. It has two plugs going into it, one bigger than the other. Have a look at that and see if it is all plugged in.
Before jumping to all this though get a screw driver and remove those door switches, see if they are corroded. They earth to the chassis with one wire, so if the car doesn't see an earth it thinks the door is open, and as such will not remotely lock.