I took my '98 Neon
which was rattling on acceleration ( lifters chattering, sluggish acceleration) and drove it down the road. It is my wife's car and it sounded awful when she left for work. Did a couple post here and nothing that seemed to help. So I got the car and drove it around. Finally, after being not impressed, I decided to "Give it hell".
I stopped at a stop sign and had an open road ahead. I pushed it to the floor and held it there. The cat SCREAMED for mercy. I said go or blow. it was blowing black smoke like a diesel. It hit 3rd at 70mph and it was red lining on the rpm's I never let out of it. I let out of it around 105 because of traffic. Drove it home and ot was a purring. My wife told me today the car was running so quite and smooth. Maybe it needed the "soot" (carbon) blown out of it.
I dunno but I believe if it won't run, sell it and if the vertical miles out number the horizontal then you got a lemon.

You could have cleanes some crap and soot out as you mentioned. A great way to do that is to use Seafoam. Google it and see what you can do with it. I have heard from people who used it and absolutely loved it.

check the headgasket if there is black smoke

check the headgasket if there is black smokeIf the headgasket is blown or leaking you check the coolant for oil, or oil for coolant. It also blows out white smoke, not black. Black smoke is oil burning, and would be time to check rings and seals.

EGR valve was probably stuck open.

EGR valve was probably stuck open.If the EGR is not working correctly, he would have gotten a Code 32. probably cleaned out the injectors.