Did you have an unemployment hearing?
What do you mean by "left the room"? Did you stay on sight? Why would they say you quit?
Age is not a requirement for disability. If your doctor willl declare you disabled they would likely have to pay it.
Your previous employer can not deny you benefits. They can only tell the unemployment people the circumstances surrounding your departure. The final decision is made by the unemployment people. You did not quit and need to be adimate about that in your statement. "I did not quit, I went to the bathroom" It should be an easy decision.
I strongly encourage you to apply. That is why the unemployment tax is paid, to protect employees who are unemployed due to no fault of their own.
You will likely not have any contact with your previous employer. The first step is written statements. A determination will be made based on those statements. Either of you can contest the findings. It would then go to a "phone hearing". You are conference called from the luxury of your own home by a mediator.
( I am an employer and have participated in several of the phone hearings)