I'd guess something is wrong with the float switch. It could just be hung up and not floating up or it could be going bad.

did you look in the pit? I thought I had pump problem w/very heavy rains in june - turned out to be the pit to where sump was emptying was failing - pump worked fine, new pit dug & stone lined

open the sump pit & run a hose to it -, if the pump is ok it should trigger discharge - depending on the setting, w/o jiggling anything.

good luck

Thanks for your suggestions. The Atlanta deluge of September 09 brought our area about 22 inches of rain in three days. The dehumidifier died. The sump pump gave up. Both have now been replaced, and all signs of dampness are gone. Music to my ears when I hear the new sump pump kick on and run all by itself!