fuel issue 13 audi a4 quattro 2.0t

[Driftxorxdie]

customer has driven this car in this condition for year to the point of no start, here are the codes and what i have done,
p0113 intake air temp 1 circuit high
p0118 engine coolant temp circuit 1 high
p0190 fuel pressure sensor circuit high
p0236 turbo boost sensor performance
p0238 turbo boost sensor circuit high
p0300 random miss
p0506 idle air control rpm lower than expected
p053f cold start fuel pressure performance
p2014 intake manifold runner position sensor circuit
p2293 fuel pressure regulator 2 performance
p2539 low pressure fuel system sensor circuit
i did not have all these codes at first due to a bad battery and the no start
i began by testing all the circuits related to the codes that i got after the battery replacement and they passed
ive swapped out the hpfp, lpfp, fuel pump module, high pressure sensor, with good known ones and nothing, the ethanol sensor was reading 50% and i was certain i had found the issue so i replaced it and it corrected the reading but not the issue so no luck there, on the live data the regulator is diverting so much fuel that its bringing the pressure down BUT at the same time its running rich!! i pulled the plugs and they are covered in soot but cylinder 4 is fauled and covered in gas so i took a look with the bora scope and it isnt getting stuck open so no luck there, fuel trims are high, at this point i believe its the ecm but i am afraid of making that call due to it being a expensive one, so i pulled the ecm and it has corrosion on it which i was able to clean with cleaner and a plastic brush, circuits are not broken and upon reinstalling it she finally started! but ran terrible and had to give it gas to keep it running, once it warms up the random miss is gone but low fuel is still there, i messed with the connector and it died, i found the wire that goes to the iat was making bad connection so i fixed it by closing the pin but same dilemma...now that i can get it started i logged some data but the software is limited to what i can see so i go back and forth from this to my autel, autel shows injector timing to be 10 ms while in open loop but corrects itself once in closed loop but low fuel is still there... so ive noticed wastegate duty cycle is stuck at 1.6%, i can move the rod so thats not stuck, im not sure what to make of that, i am at my max of expertise, but maybe the solenoid? and the actual boost reading could be off im not sure, which is where i need someone to please take a look and tell me what they think before i have them pay for a ecm. OH and does hptuners have the ability to program a used ecm to the car? damn lol i hope i didnt leave anything out i will attach the log. i begin by starting it and giving it gas till it is warm and able to drive, the miss goes away once warm but if anyone checks it out youll see it thanks in advance!