Thanks for the advice, but if I'm picturing what your saying correctly, it won't work. The screw doesn't go through the particleboard, but into it. It's the side wall (right) of the cabinet that the screw goes straight into - and the broken piece is the exterior of the side of the cabinet - the screw angled out and broke through. If it had angled to the inside, I'd have no problem just slapping some plywood or something onto the interior side wall.
What I have in mind for a fix is more of a "filler" of some kind, that would adhere to the particleboard that isn't stripped away, and allow me to put a screw through it once it's set. OR even put the screw in while it's still soft, and assume that I'll never have to remove it!