George Sofianos has presented a good suggestion. Three more:
Fiddle with the firmware
You can play with your firmware options. In particular, look for any that refer to BIOS, CSM, or legacy support, and disable them. There might also be a "boot mode" setting with options like "UEFI only" and "UEFI and legacy." If you see such an option, set it to "UEFI only." This should prevent the computer from booting the DVD in BIOS/CSM/legacy mode.
You could prepare a USB flash drive with my rEFInd boot manager (there's a download link for a USB flash drive image). Boot it with the Ubuntu CD/DVD in the drive and rEFInd should present an option to boot the Ubuntu disc. By default, this option will boot the Ubuntu disc in EFI mode.
Install in BIOS mode, then switch to EFI mode
You can go ahead with a BIOS-mode installation and then switch to EFI-mode booting by installing a suitable EFI-mode boot loader for Linux. My Web page on EFI boot loaders describes the options. Although Ubuntu uses GRUB 2 for this purpose, it's likely to be easier and safer to use something else, such as rEFInd or GRUB Legacy, since this won't disrupt the action of the BIOS version of GRUB 2, so you should still be able to switch modes by using the firmware's built-in boot manager or adjusting firmware options.
Note that some EFIs use obscure and undocumented details to determine the boot mode. Thus, you might need to experiment to get the system to switch from a BIOS-mode to an EFI-mode boot after installing your EFI-mode boot loader. Checking the firmware settings is the way to start with this. If you find that you're stuck in a BIOS-mode boot, post back with a link to the
RESULTS.txt file generated by the Boot Info Script.