The first thing that I noticed here is your carb. The 31 is very small for a 1776 engine, especially with the Engle W110 cam! I have a Type 3 with 1679 and the same cam and was adviced that the dual Solex 32 carbs were just about enough for my setup, so since you have an even bigger engine, I would look into replacing the carb.

Now, since you say that the engine runs on three cylinders while it's cold, it certainly sounds like a fuel problem since it runs good when it heats up. There is a possibility that the 31 cannot deliver enough fuel when the engine is cold and the choke mechanism is activated.

There is also a possibility that there is something wrong with the ignition system. I had similar problems with a 64 I had a couple of years ago, it didnt start at all. I replaced everything in the ignition system except the coil and distributor (which was the stock type). I ended up buying new plugs, points, rotor, dizzy cap, wires and everything else except the coil at the local VW dealer, because I was tired of messing with unoriginal parts that seemed to not work proper at all. I also replaced the gasoline and rebuilt the carburettor and the engine ran happier than ever before!

I dont know if this helps, but maybe it can shed some light on your situation?

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If you have a 5 cylinder, you don't need a stereo.

1999 Audi A6 quattro
1990 Volkswagen Golf CL Syncro
1987 Audi Coupe quattro