Well you learned a quick lesson, while you paided very little for the car, it was a 50k luxury top-line car ins 1994 and required premium unleaded gas, and that is all you should ever put into the tank. I could smack those TV idiots that say you don't need to use it. I can tell you in Cali we only have 91 octane and states that have 93 or 94 a Q will run better and get more MPG.
Good advise, try battery disconnect and see if that solves issue. If not find a good aftermarket Q mechanic and find out what the code is that your seeing. With these low miles you should be okay with repairs, but if you're looking for a car that requires to be taken care of like an Altima or Camry, buy one of those

...seriously my 97 which only gets driven 5k a year I budget $1,000 a year...if I drove more I would have to pu that to $1,500 to $2,000 easily.