First, you may want to read the following page, which describes where the relevant options are set on some computers:
If that doesn't help, one (perhaps long-shot) approach may be to use my rEFInd boot manager to boot the host OS (Windows for you):
- Verify that you've got an Intel CPU. (I know your topic says you do. I'm putting this step here mainly so that somebody else with a similar problem and an AMD CPU doesn't try this feature, which might do weird things on an AMD-based computer.)
- Download the USB flash drive version of rEFInd from its downloads page.
- Write the rEFInd image to a USB flash drive, as described in the documentation.
EFI\BOOT\refind.conf on the USB drive: Uncomment the
enable_and_lock_vmx option and set it to
true. (Note that the flash drive image has a single EFI System Partition. I'm not sure offhand if Windows will mount that by default. If not, you might need to change its type code, use Linux, or otherwise jump through hoops to access that filesystem.)
- Reboot to the USB drive and hope for the best. rEFInd should appear and enable you to boot Windows. With any luck, VirtualBox will now work.
- If VirtualBox now works, you can install rEFInd to your hard disk, as described in its documentation. Unfortunately, this is more difficult in Windows than in Linux, but it can be done. After installing rEFInd, be sure to edit
EFI\refind\refind.conf on the hard disk's ESP. You might also want to adjust the
timeout line to have rEFInd boot Windows immediately rather than present its menu.
enable_and_lock_vmx option was added to rEFInd for the benefit of Mac users who want to use Hyper-V; however, it sounds like it might work for you, too. I've never tested it for your use case, though. (In fact, I've barely tested it at all; the relevant code was a submission from somebody else.)