Hey guys, newbie here

I just got a 03 cavalier from a lady that said the engine was "seized"
I planned on putting in a junk yard motor but though I'd give it a once over. I found some EXTREMELY sludges up oil from lack of maintenance. I pulled the plugs and they were carbon and oil soaked so I replaced them. After changing the oil and changing the plugs I cracked her over.. It cranked and cranked but nothing. I sprayed some ether and nothing. I help it to the floor and cranked and what do you know? After some coaxing and wishing it finally started and ran.. I guess it wasn't seized huh? It still ran rough and blew out some nasty stuff. I noticed I could rev it up but it would die if I tried to floor it. I took it for a ride and got the same results, no power at full throttle but it ran fine at any part throttle. I put in some premium file and some gas treatment. And I also cleaned all the oil residue build up from the throttle body and air intake. It started fine the rest of the day after that, but it did have some low idle and noise below 800-1000 rpms. Two days later I went to start it but guess what, no start. Had to coax it to start again.. I am getting a check engine light and an occasional service light. I can't take the car anywhere right now to have that checked but ill be getting a scanner soon.

Any advice would help. THANKS GUYS

Oh I forgot to mention: this car only has 46k on it,,,,,