Please try starting the service manually. Please go to where you have iRacing installed on your computer (by default for Steam users this is C:\Program Files (x86)\Steam\steamapps\common folder), in the iRacing folder, look for the file called 'Start_iRacingService.bat' and double click that to start the service up manually.
You should then see a black box open and then close. After that, please re-launch iRacing.