04 BEW start issues....the list is long

Good morning all been a lurker for a little bit and thank you all for the insight you have given into these vehicles. I really love this car...when it worked. Now it is a bit more frustrating.
A little history,
Purchased in 2017 with 195k mi, CEL was reset before purchase and within 40 miles of me driving came on, car still rean great and was hitting 42-45mpg. Appeared the MAF sensor was bad. Replaced with a cheap one, didnt fix noticed no difference in power or mileage.
The real issue came while driving my brother and my son up to peak to peak highway in the Rockies. Just before we reached the summit it, under heavy load, went into "limp mode" at least thats what i believe. No real boost to speak of. all the lights on the dash came on and after a while of driving as it was, it still got 42 mpg. Just no fun to drive anymore, no boost it seemed. some other issues arose after another 20k driving.
Finally the car began to have hard starts in the morning. My ex wife actually filled with f-ing gasoline. However it started and immediately died. had towed and drained and flushed the fuel system best I could. Filled with a few gallons of diesel and got it to restart, allowing about 45 min of idle and figured there hadn't really been to much if any damage done. Since the car had 240k miles by now I read up and figured I would go through and replace the
timing belt, tensioner, water pump
cam, lifters, guides,
serpentine and tensioner,
glow plugs(light coming on and was getting a code for those with the hard start),
cam and crank positioning sensors
Throttle body
Fuel filter
after all this it now for the first time since I have owned it she throws NO CODES! YEAH! and then sad trombone sound quickly ensues upon a start and immediate shut off.
Since the the key had been giving issues with not responding when buttons for door lock/unlock I thought maybe the cutoff was being activated so I replace the battery, again to no avail.
Fuel pump works. I have witnessed it spitting fuel on ignition turn and can hear the pump as well.
I would post VCSD info...except there isn't anything.

So that's my story. And I know that without codes it is increasingly more difficult to diagnose, certainly from afar.

I have not checked vacuum and was planning to do so but have simply run out of time.

Thanks for your help all

Peace

If it starts then immediately shuts off, sounds like an immobilizer issue. The buttons on the key are a separate system and won't affect the immobilizer.

When you do start and get the shut down, does your immobilizer light stay on? It's the light that is a yellow car with a key through it.

If it's not that, check to make sure the anti shutter valve isn't stuck shut, or isn't accidentally plumbed vacuum at all times.

Which battery was replaced? The car battery or the key fob battery? Definitely you should replace the key fob battery if it hasn’t been already.

Hey thanks for the responses. @Nero morg I thought that as well but wouldn't there be lights on the dash that come on when the immobilizer is and issue? No lights. and the anti shutter, throttle body is brand new @Tdijarhead, key fob. If it is the immobilizer it is in the right place for a reprogram.

Thanks again

If the immobilizer light does not stay on, that's not the issue. IIRC if you check instrument cluster faults with VCDS it'll log an immobilizer engine shutoff fault if it was commanded to.
Only other thing I could think of, is maybe cam/crank sensor. I've heard cheap ones tend to be garbage. If you have the old ones still, toss them in and see what happens?

Try an auto scan with the VCDS. Maybe a DTC will show up somewhere.
Also might want to check the vacuum system.

Thanks for the responses gents @JB05 at the dealer now so I am hoping they check this. and I was going to buy a mightyvac but sent it in after too much time and money trying to fix on my own. I still have plans for one though as they are a useful tool regardless.