Canon AE-1 Program Help. Green P not blinking.

Hey guys, I recently bought a Canon AE-1P and I was enthralled. I got fresh batteries for it but when I switched the camera to P mode (Program on the Dial and A on the lens) the green P wouldn't blink. Everything else seems to come up such as the aperture and the blinking of the aperture and the red M but not the green P. Is it an electrical issue? Should I go to a camera shop and get a CLA on this camera and how much is it to get one done? Any solutions to this problem would be of great help.

The "P" will blink to warn you of camera shake when the shutter speed is 1/30 sec. or slower.

http://www.mir.com.my/rb/photography/companies/canon/fdresources/SLRs/ae1pgrm/html/basic3.htm