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EAC won't prevent you from logging in or playing the game, unless the server you are trying to connect to requires it.
For the EAC, you might want to try repairing it to see if this fixes your issue
https://www.easy.ac/en-us/support/game/guides/installer/
If that doesn't solve your problems, logfiles will be helpful (see the pinned topic in General Support that states "How to Report an issue")