Not helping much, but you can rule out it being Mavericks - I use that (10.9.2) and ba.com works for me on Firefox, Chrome and Safari. I assume you're all up to date with updates etc?

Are you on your own network or a corporate one? If the latter, it might be erroneously blocking something. Have you tried a different network?

Since its across all browsers, its unlikely to be this, but could you have installed a browser plugin of some sort? eg, An Ad-blocker?

Have you tried uninstalling Chrome or Firefox and reinstalling them?

And, of course...