Scribbinge

Wireless surround speakers do exist but obviously still need mains powered. i get the impression you are best sticking to a sound bar with wireless subwoofer. Something like the Yamaha YSP-2700 maybe.

Not exactly answering your question but what shape is the room and where will the TV be in it? If your TV is going to be in a corner, or the room is a weird (non rectangle) shape then a soundbar and sub would be your best bet rather than speaker surround. As far as TVs go, I'm a big fan of Sonys KD-55XE9005 which is in your budget ( on a good deal anyway)