Dome light problem

Something strange is happening with my 2000 Silverado. A couple of months ago I started noticing that my dome light wouldn't go off after I started the vehicle. Now the dome light won't come on and I noticed last week that the radio turns off as soon as you turn off the key. This is a sporadic problem.

Any suggestions on where I should begin to look? We've had really rainy weather the last couple of months. Would this be the cause?
:confused: