Having some problems with my Xbox 360?

A couple of days ago when attempting to launch Battlefield Bad Company 2 it disconnected me from Live with the message "Your connection to Xbox Live has been lost. Please sign in again." No error code, nothin. Today, the problem spread to Minecraft and even Destiny (disc based, so it isn't a GoD problem)
Xbox support was unhelpful because I spoke with Arab Ann from Pakistan. I just want to play my games, and if I can't do that Microsoft has a lawsuit on their hands.
I have a Xbox 360 ARCADE from 2009 that's had some outstanding hardware problems but this shouldn't be affected by that.
Warranty is shot, but do you think I can still get a replacement?