How to wire a GFCI duplex outlet with a garbage disposal switch & combo outlet on load?
I don't know your "switch/outlet" combination in detail, but I'd guess there might be a connection by default (ie, the switch is tied to the outlet unless you break a tab) that's getting upset by the switch being fed from the line side and the outlet being fed from the load side of the GFCI. In any case, the disposal probably ought to be connected to the load side of the GFCI.

If the switch is the same one that worked or not depending how hard it's pressed, why haven't you replaced it yet? 

The ground wire should be connected to the box. The other cable should be checked for a ground wire, and that should be connected to the box if it exists. The box &amp; grounds should be connected to the GFCI and Switch/outlet ground terminals.

If you haven't dumped the trash yet the GFCI you removed might work fine, given what you have found with the new one.