Bluekapu

First of all my names Josh and I drive a 1993 Wrx Last night I was doing the usual, driving around, on my way back home. I came to a stop at a red light, as you do. And when I went to take off again, the hesitating and stuttering started. It didn't even ease in aye, like nah it just jumped out of no where, like oh hey, I'm here to ruin your night. Any way, you go to take off in first gear and the car moves forward slowkly as per normal, you get to about 10km/h (Not as per normal) and the I start hearing popping noise, like a quieter version of antilag, or like an exhaust backfire that been trapped inside a ice cream container or something or the sort. The car has no power at this point, it chugs along slowly at 10ks but it doesnt pick up fast. I left the car for 10 minutes or so and started it again, more then motivated to get home in the rain now. It ran as normal for a small amount of time, luckily just enough to turn into my street where the hesitation started again and came to a stall pulling up the driveway. The check engine light has now come on also. I parked up for the night and went to bed. In the morning I went out to the car, not really knowing where to start or what I'm really doing in all honesty, I started by checking hoses, any and all hoses I could find. Tightened as many hose clips as I could, thinking maybe it was a air leak. This solved nothing. However I noticed that when I went to start the car up it took longer then usual, this lead me to test the battey which is holding 12.1v and 11.2 under load. Aka, flat as hell. I currently dont own a battery charger or a spare battery, but before I go off buying these things, could it be a plausible reason that my car is doing this? What else can I look at? Injectors? Colis? Spark plugs? Map? Ecu? Pretty lost atm, all I know if baby rex is broken and thats not okay. Any help much appreciated