If your computer shipped with Windows 8, it's likely that you're running into Secure Boot limitations. If this is the case, the easiest solution is to disable it;
however, there are other options (described elsewhere on that same page.) Be aware that signed versions of shim are now available, which makes that approach more practical.
If your computer didn't ship with Windows 8, I'm not sure precisely what might be causing the problem, but I do have a couple of suggestions for how to proceed:
- Try installing rEFInd, which is a boot manager for EFI systems. It should give you the option to boot Windows or, when you insert your Mint disc, Mint. It's conceivable that this boot manager will work around whatever limitation is causing you problems; however, there's no guarantee of that. Given your setup, you'll need to either install it manually from Windows or boot the Ubuntu disc in try-before-installing mode, do a "sudo apt-get install efibootmgr", and run the rEFInd installation script (install.sh).
- Go ahead with a BIOS-mode installation and then convert to an EFI boot afterward. Having an EFI-bootable Linux (like Ubuntu's installer) can help with this conversion process, since it's very helpful to be able to use the efibootmgr utility. See my Web page on EFI boot loaders for information about your options. Mint uses GRUB 2 by default. IMHO that's a poor choice, but since it's the standard for the distribution, it's got an edge in ease of installation and maintenance over most others.
Some partitioning tips for your installation:
- If you install in BIOS mode, create a 1-2MiB BIOS Boot Partition. This is semi-required for BIOS booting, but useless in an EFI-mode boot. Fortunately it's small, and it won't do any harm once you've switched away from a BIOS-mode boot.
- Create a separate /boot partition of 200-500MiB and use ext2fs, ext3fs, or ReiserFS on it -- not ext4fs or other more sophisticated filesystems. This isn't required for most configurations, but it can help with some, particularly if you use ELILO or the kernel's EFI stub loader as a boot loader.