I have an 06 STI. And Im no machanic I was just trying to use logic. So I was pulling out of my work parking lot and my car started to studder as I pulled onto the road going into 2nd gear. I looked and my fuel level was low. (I have been actually running it lower than I normally would due to finances at the moment) So my first thought was to get gas. So while still studdering I pulled into the nearest gas station and filled up. I had trouble cranking at the gas station but it finally cranked and I started off down the road when the studdering got worse and the car basically choked out. I could get it cranked but it would bog out when I pressed the gas and cut off at idle. I sat for a min and could not get it cranked again and the battery died? So I bought a new battery still doesnt crank I checked all fuses. So I ask around and the general consensus was fuel pump. So I bought a new fuel pump. Got the fuel pump in and it cranks fine but idles extremely rough. Backfires when revving. It will only rev for a 20-30 seconds after being cranked after that it bogs down and cuts off. And its the same if I just crank it and let it idle it will idle fine for a few seconds then down and it will catch it self 2-3 times before it chokes out. I dont know exactly what to do or where to look for the problem. Spark Plugs? Injectors? Fuel Pump Relay?