After massive coolant leak, terrible idle, black smoke. still in trouble

[Martin Pot]

Hi Guys.
I am still at a loss here with the 2CTQA 20v 3b engine, and this has been
the longest period of time I had an Audi down in 10 years, and it has become
embarrsing.. I have measured the RPM sensor and ignition sensor per Bently
and they seem to check out good.
 I have finally managed to  pull the codes but I am getting 4444 with my
blinking light, while the car is struggling to keep alive. I did not take it
for a drive before I did the codes, may be that is the problem, but I am
afraid to drive the car as it is. When it idles it sounds like vvroomm,
vvroomm, vvroomm with a slight pause in between the vvroomm's, and very near
death only to struggle back up to a burst of 900 RPM. It is also producing
nasty black smoke, but gets less when I rev the engine but still keeps on
smoking.
 It seems it is getting way too much fuel.
If the fuel pressure regulator fails would this be the result?
It is driving me nuts not to be able to find the problem.

Thanks, Martin.