2003 Hyundai Elantra can the car fail inspection

Until you verify which codes occured, your guess is as good as mine. Whenever the 'CHECK ENGINE' light comes on, the ECU (Engine Control Unit) sets a Diagnostic Trouble Code (DTC). These codes identify the particular engine management system which caused the light to come on.
You'll need to use/find an OBDII (On-Board Diagnostic) Scanner to retrieve any code which have been stored in the ECU computer. Afterward, we might be able to help you DIAGNOSE and perhaps eventually fix the problem.