Ok. Things seem a little clearer now. Sounds like it was a bit of a mess at the airport that day.
But I still have lots of questions.
You arrived at check-in 2+ hours before departure.
There was a line. You waited 45 mins. Did you not try one of the mobile check-in machines? Were you checking baggage?
Given that you were now approx 90 mins from departure, did you ask at the check-in if you could have expedited or priority security access given that the lines seemed long?
Once you had your BPs (boarding passes), it took you another 90 mins to go through security?
Did you speak up at any point and ask to be moved to the front of the line given that your flight was closing? If you didn't, then that's on you.
When you reached the gate (and it sounds like the flight had closed?) who did you talk to? Did the agent re-book your ticket?
You said you bought a new ticket. Who told you to do that? Did you call Aer Lingus on the phone? Or did you go back to the Aer Lingus ticket desk in Departures?
Basically, this sounds like a Brussels Airport issue ... and doesn't qualify under EC261 for a claim against the airline.
Though, Aer Lingus might be a bit more sensitive to your inconvenience.
Also, did you have travel insurance? This is a situation where travel insurance would come in very handy.