Yes the cps only controlls when the coils and ignitor fire the spark plugs.
There is a little 14 gauge wire that runs out the back of the starter. CHeck that for either being gone, corroded, or loose. Thats the signal wire.
There is a main batter ground, a fuse box ground, a block to chassis ground, a head to firewall ground, and a cpu ground (4 wires total, 2 white 2 brown) under the intake mani.
I *think* thats all the grounds.
There is a relay up under the pass side of the dash also... but I wouldn't think of it as the culprit.