JMHershey125, have you had the opportunity to check with your dealer yet about this concern? I realize you're likely seeking DIY advice, but please feel free to send me a private message anytime if you would like me to check for recalls, etc., that may be open on your Impala.
I just checked my '08 impala and their is no button to turn on the dome light, but it will turn on when the curtisy lamp dial (this is the dial that pops out next to the headlamp switch) is turned all the way to the right. Their is two switches for the two map/reading lights in the rear view mirror and the two map/reading lights in the dome lamp assembly. The dome lamp itself is the middle light in the dome lamp assembly. You may just have a bulb that is burned out.
There are 3 lights in there, 2 reading lights, and 1 dome light. The dome light comes on with the doors, the reading lights do not. I would guess your dome light is burned out, the plastic cover is just snapped in place, there is a notch in the driver side of the cover, slip a small flat screwdriver in there and pop it down.
Sometimes bulbs last so long, we forget that they burn out. I have had my car for 16 years, and still haven't had to replace the tail light bulbs. If I didn't work on a fleet for a living, I would probably freak out and start checking wiring if I finally lost one.