It's hard to guess without being able to do some basic diagnostic tests. I would first check for fuel pressure on cranking when the engine won't start, if it doesn't start and have fuel pressure check for power at the fuel pump on cranking,if its got fuel pressure check for injector pulse. The injector should have power at on side ignition on and the fuel injector then gets triggered by the fuel injection computer.With a scan tool it would be interesting to see what the computer sees as engine coolant temperature, cold temperature should enriches fuel mixture on starting. There is a company that independent auto repair shops get their information from, this same information is available inexpensively for people that work on their own cars.. The information is year make and model specific, covering repair procedures, torque specifications, fluid capacities and specifications, service bulletins, component locations, wiring diagrams ect.... Alldata is very easy to navigate http://bit.ly/AllData_Repair_Manuals_Online
Hyundai as a car manufacturer put a lot of free technical information and workshop manuals on line for Hyundai owners. Check out www.hmaservice.com lots of great information(not sure they go back that far).