There would seem to be two issues here:
1) Cold enrichment
2) Possible timing problem

The distributor initial position is set by bringing the engine to Top Dead Center (TDC) on #1 using the mark on the harmonic dampener. When the engine is at #1 TDC the rotor should align with a mark scribed on the rim of the dist. housing.

Manifold pressure (vacuum) is supplied to the ignition control module (EZL). All timing adjustments are made in the EZL on the basis of engine speed and manifold pressure. The distributor serves only to distribute the sparks, although it does contain a centrifugal mechanism to ensure proper rotor phasing as the spark timing is advanced.

Based on the appearance of the cap and rotor replacement is in order.

With all ignition matters corrected, including the wires and spark plugs, there is still a possibility that an engine sensor is defective, causing the mixture to be lean. Sensors include water temp, air flow sensor position, over voltage protection, engine speed, road speed signal, O2 sensor, and altitude correction.