The keyless entry and dome light are all controlled by the same
module. The module depends on inputs from the door ajar and trunk ajar
switches in order to control keyless operation and lighting. If the
trunk ajar switch shows ajar for a long period of time, the module has
logic to shut down the dome light to prevent the battery from running
down. The logic also prevents the keyless entry from working when the
trunk ajar signal is present.
Since the lights and keyless are all tied together, and the clearest
indication of a problem is the "trunk open" message, fix the trunk
latch switch first. The dome light and keyless entry will start
functioning properly again once the trunk switch reads closed.