The door light plunger switches are either missing or disconnected. Real common issue so the dome light stays off when the door is opened, supposedly a safety measure at night when cops are in the car. Easy enough to hook back up, just may have to buy a couple switches if they are missing. - Peter
Check to see if they are hooked up. The only reason the fronts will not work and the rears will is the connection when you open the front door. Both switches may be broken. You can test them by taking the wires off and touching them together. The switches are very inexpensive. You have to take the carpeted kick panels off to get to them.