Im not sure if the BT and WiFi are driven by the same card but as a minimum Id guess it has been apart and the antennae havent been reconnected properly...
I am beginning to think we have something really funky going on here. Is there anyway you can get this to a Genius Bar? The consultation is free and most software reimages are free.
Since your Mac isn't listening to commands at start. Try going to System Preferences (with Mavericks USB attached) --> Startup Disk and see if it appears there. If so, select it and reboot. Follow the steps from earlier!
Remember, you will lose all data in the process. Also, the Mavericks installer likes to say "About a Second Remaining" for a while. Don't worry it didn't hang. Just let it be!