The problem is, that the engine would not even start any longer. Starter goes on, the engine gets some power and then immediately idles. So, I can't get new codes (was told that in order for the codes to be updated, the car needs to run for a while). Sorry - I did not properly described the issue.
Once in a while it does run for 10-15 seconds with no power (I push accelerator into the floor with no results).
I did install new set of coils and plugs after the problem appeared and it did not change anything.
Another thing that I did not probably mentioned, - is that the car was sitting in my garage for almost a year with the tank half-full. After that it was running, but was idling quite often on stops. I was advised to add fuel conditioner, which I did together with new fuel. I was running on the same tank when problems started. That is why I am asking - could it be just remains of that fuel causing the issue? I know it sounds silly, but still..

Speaking of which - is there any simple way of draining the tank?