Inferring from the rated fan and pump speeds of the Corsair H100i, I would expect your system fans are configured as so:
CPU - one of the fans on the H100i radiator
CPU OPT - the H100i pump
OPT Fan 3 - the other fan on the H100i radiator
CHA Fans 1 & 2 and OPT Fan 2 - Case fans?
Anyway, unless the pump is actually plugged in elsewhere and isn't being read at all, it would appear to be working.
Either the fins on the waterblock's cold plate are clogged (it's a mixed copper and aluminum loop which requires inhibitors in the coolant to forestall galvanic corrosion and these are likely depleted by now), or the radiator is so packed with dust that it has nearly zero air flow. It's also possible that something has happened to one of the mounting screws and that the block has lifted off the CPU partially.
Another possibility is that the radiator is in the wrong orientation. If it's mounted to the front of the case with the barb/hose side up, then there is probably an air pocket at the top causing the pump to ingest air rather than water. I'm doubtful this is the case because the impeller in these pumps needs to be submerged to work correctly...running them dry will damage the bearing and eventually cause them seize up, but yours seems to be running at normal speed.
Anyway, you'll find out for sure when you take it a part.
Chances are the CPU and board have survived, because of the ability to thermal throttle, so getting the CPU cooled properly should be all you need.