Why won't my mouse button click?

The mouse button (not the whole trackpad, or the keyboard, but just the mouse button) has decided that it's permanently depressed, which means I can't click on anything anymore. It's definitely a hardware issue; the same thing continues if I boot into Ubuntu.

The computer's too old to merit the couple hundred dollars it would take to replace the whole upper case, so I wanted to see if anyone had any other ideas about how to fix this. Is there a connector somewhere that could have gotten loose? Is there something I can try to clean? Etc.

Wild ideas welcome.

Thanks!