If you're BIOS has the option try switching from UEFI to Legacy.
Edit: I just reread and noticed you're not running UEFI. Ignore the first sentence above.
Backup Windows partitions. No need for Ubuntu partitions backup since apparently fresh install.
Switch BIOS back and launch live CD then chroot into your Ubuntu install again as you did before.
Install EFI bootmanager
sudo apt-get install efibootmgr
A list of your partitions should come up. Make note of the numbers used for Windows and Ubuntu root.
Set Ubuntu to boot first. If you're numbers are, for example, Windows=1 and Ubuntu root=2 run:
sudo efibootmgr –o 2,1
Reboot and you should have a boot menu to choose from.
Edit/Notes: It's not clear why you are using GPT without UEFI. Windows sets up a GPT partition table when it's installed while UEFI is enabled.
https://msdn.microsoft.com/en-us/library/windows/hardware/dn898510%28v=vs.85%29.aspx
Otherwise it sets up a MBR partition table with UEFI disabled.
https://msdn.microsoft.com/en-us/library/windows/hardware/dn898504%28v=vs.85%29.aspx
Did you install Windows 10 while in UEFI mode and then switch? If you did and then switched the mode to legacy after and if this is a fresh install for both, which it sounds, you many want to start over and switch your BIOS to UEFI from the beginning to end if you want to use GPT. You may still need to install efibootmgr and change the EFI boot order after installing Ubuntu or if your BIOS has the option you can change it there.
Otherwise if you're not going to use UEFI you should start over and install Windows without UEFI enabled and install Windows 10 with MBR partition table. Then install Ubuntu and use GRUB.
Almost forgot...make sure Windows Fastboot is disabled. It's like a always on hibernate at shutdown. It can prevent loading other operating systems and if you do manage to load another OS there's a potential for corruption of the Windows system. The link below is Windows 8 but still applies to 10.
Why disable Fast Boot on Windows 8 when having dual booting?