Sadly, you do have to get a micro USB cable, as did I today after last night having the exact same issue (as many others did). I did manage to get one on sale at Best Buy for $5.00, and it might be handy to have around. Having restored my Apple TV 3 and re-entered all my settings and accounts it is working again, but if you have updated to IOS7 on your devices, etc., you may find that airplay is not working much, if at all--I have just posted a discussion on this, I suspect there are problems with both updates (IOS and Apple TV) and AirPlay. FYI.
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