Car clock stays on and runs through the numbers like I were setting it.. help?!

What is your question?

I have a 2001 Chevrolet Prizm that seems to be having some sort of electrical issue. The car clock stays on even when the car is off - it also flips thru the time uncontrollably like I were trying to set the time. Any button on the dashboard stops it and causes the clock to go black but once the button is let go - there is a clicking sound and the clock comes back on and continues malfunctioning. I would be fine with removing the radio circuit and going without it if it means my car battery won't keep dying.