LL:

Cold starting of an engine equipped with K-Jetronic is dependent on three things: 1) fuel pressure, 2) the cold start injector, and 3) the control pressure [which is governed by the control pressure regulator, usually called the warm up regulator (WUR)].

If the key is cycled OFF/ON a few times, you should here a change in the tone of the fuel pump as pressure is built up. Yes?

The cold start injector sprays fuel into the intake manifold when the temperature is below approx. 20C and the starter motor is engaged. The spray continues for a second or so after the starter is released.

If the WUR is stuck closed, or the fuel lines to and from the WUR are clogged, the control pressure will be unusually high, which will cause a lean condition, and difficult running after start. If the WUR and the lines are open, the default condition of the control pressure is low, which will cause a rich condition (good for starting).
Blocking the WUR will cause a very lean condition.