There are two issues that I suspect you're conflating:
- EFI/UEFI -- The Extensible Firmware Interface (EFI) and its more recent variant the Unified EFI (UEFI) is a successor to the ancient Basic Input/Output System (BIOS) firmware. Linux installs fine on EFI-based systems, although there are still bugs, quirks, and gotchas of various types. Most modern UEFI-based PCs also provide a BIOS compatibility mode so that you can boot in either way. If you're trying to dual-boot with Windows and Windows is already installed and working in EFI mode, you should definitely use EFI mode for booting Linux; switching boot modes is awkward at best on most systems.
- Secure boot -- This is just one optional feature of UEFI. It's a recent addition to the UEFI specification, and as of yet, I don't know of any computers that ship with secure boot support. (I could well be unaware of some new system that uses it, though.) Microsoft will require that secure boot be enabled on computers that ship with Windows 8 in order for those computers to get a Windows 8 certification.
My suspicion is that you ran into a UEFI compatibility issue, disabled UEFI in your firmware, and then ran into some other compatibility issue. If so, this has nothing to do with secure boot, and in fact it might be better for you to try to resolve the issue in EFI mode, particularly if you intend to dual-boot the computer.
Moving forward, I recommend you answer these questions/perform these tests:
- Do you plan to dual-boot with Windows?
- If you plan to dual-boot, how is Windows booting, in BIOS mode or in EFI mode? You can find out by typing "bcdedit" in a Windows Administrator Command Prompt window and looking for the "path" line in the "Windows Boot Loader" section. If this line refers to winload.efi, then you're booted in EFI mode; if it refers to winload.exe, then you've booted in BIOS mode.
If you're currently booting Windows in EFI mode and you plan to dual-boot Linux and Windows, then your best bet is to get Linux to install in EFI mode. Alternatively, you could install Linux in BIOS mode and switch boot modes after installing.
The Ubuntu installer should start up in EFI mode, but precisely how to get this to happen varies from one firmware to another. You can verify that you've booted Ubuntu (including its installer) in EFI mode by checking for the /sys/firmware/efi directory -- if it's present, you've booted in EFI mode.