Since your desktop came with Windows 8 preinstalled I believe you already have an EFI partition.
While in the live DVD Ubuntu session try to get gdisk installed via apt-get, and list the partitions with
sudo gdisk -l /dev/sda.
The partitions would be most likely in this order
- A small, under 1MB partition with code EF02
- The EFI partition with code EF00
- A windows Recovery Environment partition, code 2700
- A windows System Reserved partition containing the BCD, MSR code 0C01
- followed by the OS partition, perhaps code 0700
These short codes are gdisk's internal, in the GPT they have GUID corespondents.
If this is the partitioning scheme that you already have, you can leave the first four partitions untouched and either shrink or delete the Windows OS partition to make room for Ubuntu partitions. To shrink you'll have to get gparted installed, otherwise for deletion/creation you can stay within gdisk. If you deleted everything try to recreate this partitioning scheme under gdisk.
edit You can also do the partitioning from within Windows Disk Management, shrink the Windows NTFS partition and make the linux partitions, leaving them unformatted and with no assigned letters, then in the Ubuntu installer just assign them their respective mount points, type and format. It is potentially safer to continue partitioning the disk using the same tool that it was started with. /edit
About your blank screen, you might have a graphic card that still uses old BIOS functions, try to temporarily enable BIOS compatibility while doing the install, and make sure that you are booting your DVD under UEFI. If you boot the DVD under BIOS while trying to do an EFI install you might get into GPT issues.
If you install your Ubuntu with grub-efi-amd64-signed I believe you won't have to turn secure boot off.