Your thread says you are running Windows Server 2003, but the text in your thread says you are running Win10 Home -- so which is the case?
Also, the OS running has NOTHING TO DO with installing any Linux distro. You do not install Linux from withing a Windows OS, but instead, boot into the Linux installation media to intall the distro -- and in that case, the Windows OS is not even running.
However, Win10 uses a new Hibernation process, known as Fast Startup, such that, even when Windows is not running, the Windows filesystem remains mounted -- and that will prevent any operations that require changing the sizes of the existing Windows partitions to create room for Linux.
HP only warranties their PCs for usage with the OS that comes preinstalled. IF you replace that or add a different OS, then you assume full responsibility for maintaining that other OS -- as HP then provides no assistance on that.