Electrical background also, perhaps I can give you some input that 'might' help.
I don't have the electrical schematics for your vehicle, and I think that is going to have to be a priority. I do however have some Camry schematics, and picked a 2000 to get relative same age technology.
The door locks appear to be coordinated by an 'integration' relay. On different vehicles I've seen integration relays on the main junction block under the dash, but also behind the left kickpanel, and I think I've even seen some vehicles have it in the right kickpanel. Where yours is, you'll have to search for. There are also two different types of integration relays in the Camrys, one made from TMC, and one made from TMMK.
I think the significance of the key in the ignition, is that the door locks are supposed to do something different if you leave the key in the ignition, to prevent you from locking the keys in the vehicle.
The fuses to circuitry that the integration relay is in are a 7.5A dome fuse, a 30A power fuse, a 25A door fuse, and 10A gauge fuse. The 'power' relay is also in the circuitry.
I guess what I would suggest is to check all of those fuses (meter them out) to make sure they are okay. Beyond that, I'm not sure what you'll be able to do without the schematics....unless you just want to take a shot and replace the integration relay. Don't know how much that is.