After some McGivering, I popped out the connectors, stripped off the last 1cm of brittle wire, twisted on the wires from the harness, inserted them into the connector, crossed my fingers and started the car. Bingo!
Anyways, what the hell does this connector go to? It's on the right side of the engine and obviously the car won't run w/o it connected.

I need to get a new grey connector that goes into that harness, which shouldn't be too hard. What should I do about those brittle wires though? They go back into the main wiring harness, so cutting them off and soldering on new ones will just move the problem somewhere else, right? What are my options?