I made a few posts with this proposed solution this evening. a Lenovo driver, updated for Windows 10, worked on my E6400 with a Dell 370 BT card (Broadcom chip). I believe that the Lenovo driver works on many Broadcom-based BT cards. First, uninstall any BT software that mah have partially installed. Install the Lenovo driver from the following link. After that, even the driver from the Broadcom site will install, if desired.    support.lenovo.com/.../ds031759   [URL] A [URL]      
I see that everyone that upgraded to Windows 10 are having issues with either WLAN or Bluetooth wireless or both.  My computer is a Studio 1735 with an upgraded network card and was running Windows 7, 64b OS.  After upgrading to Windows 10 everything worked great except Bluetooth.  It does not even show up anywhere except the little light on the keyboard display.  The fingerprint thingy hasn't worked since I installed Windows 7 but didn't use it anyway. By the way the only Bluetooth device I used was a Dell travel mouse and I went to Best Buy yesterday and purchased a Logitech $12 wireless mouse which works fine.  I just would like to get the wireless Bluetooth working in case I decide to use it later. Forgot to add, my upgraded wireless card is a 5300 PCI Express Internal Half-Height Mini-Card.     
Windows 10 Bluetooth Problem