The fob may not working because the car 'thinks' the boot is still open . It disables central locking because the car would not actually be fully secure. When you solve the boot sensor problem I think it would again central lock from the fob. .
But I dont know how to fix the boot sensor.
Older cars may have a simple plunger switch . These can sometimes be adjusted,either by screwing the plunger in or out , or by adjusting the 'plate' where it makes contact. The wire to the switch might be loose or corroded, or the switch might have a poor earth to the car bodywork due to rust etc. . But newer cars may detect by sophisticated electronics, way beyond my knowledge. I dont know what your car has.
Its possible the rear wipers and boot switch are connected - perhaps literally by a wiring short circuit or something.
