The "detailed specs" PDF on the page to which you linked indicates that the computer originally shipped with Windows 7, perhaps in 2012 (one document bears that date as a copyright). As such, it might use BIOS firmware or (U)EFI firmware. I don't see any other clues as to which it might have been. Even if the computer is EFI-based, it likely does not support Secure Boot, which would explain why you can't find such options. (Most manufacturers added Secure Boot support with computers that shipped with Windows 8.) In theory, Ubuntu should boot with or without Secure Boot enabled. In practice, it usually works either way, although there are some very rare situations in which Secure Boot can prevent Ubuntu from booting, and somewhat less rare situations in which Secure Boot causes other problems (like difficulties using third-party drivers).
You've neglected to mention three critical pieces of information:
- How did you create the USB drive? Most methods of creating a bootable USB drive from an Ubuntu installation
.iso image work on some computers but not on others. Switching from one program to another may fix your problem; or you may be able to adjust options within a single program. Personally, I generally use the
dd method of copying the
.iso file to a USB drive. If you're doing this from Windows, Rufus seems to work better than most -- but Rufus also offers options that you may need to adjust. See this page of mine for more on this subject.
- How did the boot fail? You say that the attempt to boot the USB drive failed, but you provided no details. Did the computer not recognize that you had a bootable USB drive? Did it start to boot the USB drive but then hang? Did you see an Ubuntu logo at any point? Did the computer spontaneously reboot? Did it show any error messages? Any detail might be helpful in diagnosing the problem.
- What version of Ubuntu are you using? You did specify Ubuntu server, but not the version number. As a general rule, the more recent the Ubuntu the better. That said, your computer is old enough that it should work with anything that's currently supported, so this may not be important unless you're using something truly ancient and unsupported (like Ubuntu 10.04). OTOH, there might still be a bug or quirk that could require use of a particular version, or to avoid using a particular version.
Given the information you've provided, my only solid advice is to try another tool for creating a USB flash drive. If that doesn't help, please clarify the above questions. Also, please check the firmware setup screens for any mention of "EFI" or "UEFI" options, or for "legacy boot" support. If such options are present, your computer is likely EFI-based, and so can probably be booted in either BIOS/CSM/legacy mode or in EFI/UEFI mode. One method might work better than the other. If you can't find such options, the computer might be a BIOS-only system, in which case solutions based on EFI-mode booting will likely be useless to you.