Hi,
If it's just a software issue, hopefully you can get a solution from ASUS support without sending it back.
You may also want to go to
www.asus.com to choose your region and look for support information, but you can try this page too:
http://support.asus.com/Hotlines.aspx?SLanguage=enSorry, I don't have the G750JZ model, but did you arleady try installing the bluetooth driver from the ASUS G750JZ download site and did it give you that error in the screenshot you provided?
Make sure to install the ATK and chipset drivers too from the ASUS download site in case they have anything to do with this and check your device manager for any errors.
Good luck!