Welcome to Flyertalk, welcome to the British Airways Forum. It's good to see you here
TownCar, and as somone who is also NCL based I hope we see plenty more of you.
By sheer coincidence I booked a NCL to EWR on ba.com earlier today, going out 25 October, returning 6 November. It went through smoothly, and I've been ticketed already too. I've just tried it again now, for 9 October and I get to the point of being able to pay a deposit to hold the flights. So I don't think there's anything majorly wrong here.
1) Try a different browser, Chrome works best for me, or even Incognito mode of Chrome.
2) If you don't mind a 2 hour wait at LHR (not necessarily a bad thing) then try the Multi City tool, entering NCL-LHR then LHR-EWR and then the return details.
3) Try calling BA first thing tomorrow morning or lunchtime tomorrow. They tend to be good times to get through.
4) If you have Skype on your Smartphone, try calling the Tokyo office or Hong Kong via this tool:
http://www.flyertalk.com/forum/briti...ntly-open.html
There is now a direct service with United from NCL to EWR but unfortunately it is summer only.