2003 Honda Civic. No dome light when drivers door is open. No 'lights on'...
 

...chime when key out and door open?? The interior light does not come on when the drivers door is open. It does with other doors. Also the chime that indicates the lights have been left on does not work when the drivers door is open. Can't find a fuse that would relate to this. Any suggestions???

Take it to an autoshop. Best advice.

Is there a little button in the door jamb by the hinges? Alot of times these get stuck or damaged by moisture. Sometimes you can work them loose, maybe a little squirt of somthing. to clean it off. Thats what it sounds like to me.

the switch in the door is not working

Look where the door opens for a little covered spring. It could be bent or broken. The inside of the door where the spring touches could also be dented. Before spending $80-100/hr at a repair shop or jumping to conclusions about wiring, check these things out.

Okay then what about the 'lights-on' chime not working?
 

I have a 2003 Civic with the exact same situation described as simjam in the original post. My gut tells me it's electronic-- something in the ECU maybe-- rather than mechanical (the doorjamb switch). Like simjam, I have eliminated fuses as the problem too. Could it be an update to the ECU or something? I would like to know before I take this thing into the shop and they tell me 'ah, basically you need a whole new computer.'