EML, DSC, and Brake Light (Amber) came on car went into limp mode.

What is your question?

EML, DSC, and Brake Light (Amber) came on while I was driving and the car went into limp mode. Pulled over turned off the car and it was fine. Then it happened again the next day only when I drive far around 10-12 miles. I got the error codes: P0171 = Fuel Trim, Bank1 System Too Lean P0174 = Fuel Trim, Bank2 System Too Lean P0303 = Cylinder 3 Misfire Detected P0304 = Cylinder 4 Misfire Detected I found a hole in the Lower Intake Boot, could that be the reason why the car went into limp mode with the EML, DSC, and Brake Light (Amber) coming on? The guy at Autozone said that my battery was also bad and it needs to be replaced. I also recently installed New Headlights and HID kit to my car. Could the hole in Lower Intake Boot be the cause of the car going into limp mode or could it be something else?