2005 Toyota Corolla Air intake

2005 Corolla S with about 35,000 miles on it. Tried changing the original stock air filter with a whole new aftermarket system. Tried hooking everything up and we didnt know where the hose went. During the attempt of installation the chip or piece with the wires that goes into the intake pipe touched the battery and there was a spark. Didnt know if that friend the wires or something or if it affected the car at all We tried starting the car and it didnt want to start. It kept coughing. So we decided to put the stock filter back on and we did making sure everything went back. The car started a little stronger but it still died on a couple of the stars. We took it for a short drive of about a mile and the car died about 10-15 times. Whenever we tried to accelerate or step on the gas just a little, then the car would shut off and we would have to start it back up. If we pressed the pedal very slowly then it would be ok and wouldnt stall as much but sometimes you would hear this really weird noise like cough. Maybe there isnt enough air getting to the engine or the chip that goes to the intake is messed up. Please help beacause this is my friends car and we want to find the problem. Thank you very much!