The grub menu comes up and offers you a choice of systems to boot. When your selection is made, grub either hands the boot process over to another bootloader (as in windows), or calls the kernel image in the /boot directory (as in Linux).
The power is on at first, then shuts off. That implies something in your system setup: either in the kernel configuration, or in one of the boot scripts or module loading.
I gave you a suggestion for a google search to a possible solution. You may need to install some bluetooth specific software utilities.
Here is the link to one article that I thought particularly applicable to your situation: