I am looking for some help with my non-modded 02 Impreza RS.

A few weeks ago upon a cold start my car started running rough, typical feeling of a misfire. I only got a minute or two from the house and it threw a code P0303 (#3 misfire). I brought the car back home and let it sit for a while and tried it again and it ran fine so I cleared the code and was ok for a few days.

Eventually it happened again but this time threw no code. Again, I used it for about a week and a half until this morning when it got worse.

It cold started ok but after a mile of driving it started the same misfire type running, hesitation poor idle and eventually got worse to where it seemed like it was running on half the cylinders or less. I was able to turn around and barely made it home. The odd thing is that at one point I shut the car down and restarted it and it ran fine for a few seconds (maybe 30-45) but then started running rough again. The car had new plugs and wires about a year to 2 years ago so I thought perhaps it was a coil pack.

I tried that later in the day and the car ran ok for a little while until it eventually started running terrible again after I got on it (70 mph @ about 4k) again it was a struggle to get home. I again shut it off and restarted it and once again it runs ok for a few seconds then it starts running rough/misfire. I was able to repeat this a few times. And all this time no CEL. But I then checked the codes again and found a P0734 (4 gear incorrect ratio). I once again cleared it, put back the old coil pack and took it for a ride 2 times and it ran well but I didn't get on it, just drove normal?

At this point I don't think plugs, wires or coil are a factor. Possible fuel issue? Would be interested to hear from members with far more experienced than I.

Thanks!