Well it sounds like you've already found the problem - the input jack.
Most pedals I've worked on have a stereo input jack - so that when you plug a mono jack into the input it shorts the ring (connected to the battery negative) to the sleeve (which is ground) which turns on the pedal. The footswitch just switches between the effect and bypass.
I suppose it could be a bad contact with the case as you stated, in which case a simple continuity test between the grey wire on the input jack and the inside of the case. It couldn't hurt to do the same on the output jack, because that doesn't have a sleeve/ground wire, because it is also in electrical contact with the case.
Either way, with these things, it is often a mechanical failure - the switch, the connectors, or the knobs, things that move. The sockets generally take a bit of a beating, with regular use, and years of rough "stomps" that can hit the jack plug. I'd just replace both the sockets, they look to be fairly standard - just remember, you'll need one stereo, and one mono, although you could just use a stereo on the output, as you're only connecting one wire to the tip.