Check to see if you can launch a TEST session.

Here are some things that could be causing this issue:

It could be your antivirus or firewall software causing this issue.
Please be sure these files are being allowed through your firewall and/or antivirus software 

C:\Program Files (x86)\iRacing. 
C:\Program Files (x86)\iRacing\iRacingService.exe
C:\Program Files (x86)\iRacing \iRacingSim.exe
C:\Program Files (x86)\iRacing \iRacingSim64.exe
C:\Program Files (x86)\iRacing \iRacingLocalserver.exe
C:\Program Files (x86)\iRacing \iRacingLocalserver64.exe
C:\Program Files (x86)\iRacing \iRacingChat.exe
C:\Program Files (x86)\iRacing \iRacingLauncher.exe
C:\Program Files (x86)\iRacing \updater\iRacingUpdater.exe ******

Reboot your computer

Log back onto the members site and try to launch a test session.

Do you have a program on your computer called: Qualcomm Atheros Killer Network Manager?
You can check this if you go to your Windows Control Panel...Programs - you would see it listed there.
If so, you need to go into that programs configuration settings and make sure all of the above iRacing files are allowed through as well.

Please try and navigate to your Documents/iRacing folder and open to edit the core.ini file.
In the core.ini, change the value of connect_sockets from 0 to 1 and then save the file and try again.
If this doesn't resolve the issue, please change this value back to 0