2003 Chevy Truck battery goes dead

I have a 2003 chev 2500 HD 6Lt gas Lbox auto. 4x4. The battery goes dead if it sits for a few days. What I have seen is that after I use it, and it sits for an hour or 2 the digital odometer lights all come on. Then if I open the door they go out like they are reset, but after another hour or two they come back on again. It is the whole digital display square that lights up not idividual nummbers. Thanks for any help you can give me