Had this happen to my receiver as well. Happened to be a broken fuse, which should be easily mended with a soldering iron. I'll just leave this how-to here: http://replayproject.wordpress.com/2010/10/09/how-to-repair-microsoft-xbox-360™-wireless-gaming-receiver-for-windows®/
I did use another how-to, this one seems overly elaborate. Basically just pry it open, find the fuse as designated on the board and solder it.