Help us help you. By posting the year, make, model and engine near the beginning of your help request, followed by the symptoms (no start, high idle, misfire etc.) Along with any prevalent Diagnostic Trouble Codes, aka DTCs, other forum members will be able to help you get to a solution more quickly and easily!
A faulty coolant temp sensor can cause a hot crank-no start with fuel and spark.
PCM thinks the engine temp is -40° and gives it WAY too much gas for a hot engine.
I like your EGR theory too. When I suspect an open EGR on something with no data I remove the valve and block the port with a piece of cardboard, gasket, beer can what have you and see if the symptoms improve.