1992 Jaguar Vanden Plas back firing through the air cleaner

Hello I just purchased this 92 jag it has the 4.0 in it and when you first start it it runs real ruff like its missing then it smooths out but if you try to accelerate it will back pop through the air cleaner box. Sometimes it will rev up and run beautiful you can hold it around 3,000 and no missing just a smooth running car but most of the time it either try's to stall or it pops. The guy I purchased it from has had to unplug the batt, every time he shuts it off because of the dome light it wont shut off. I don't know if this affected the computer or not.