Greetings Sim96,
Welcome to the forum.
I am not an HP employee.
You have a couple of roadblocks to deal with.
The h8-1250a was released for sale by HP in 2011. This means you have Legacy 7.xx version BIOS. The newer graphics cards require a UEFI BIOS.
The PSU included with your PC is 300 watts. I don't know what graphics card you tried to install but some graphics cards require more than 300 watts.
Your PC shipped with a PCIe 2.0 x16 slot. New graphics cards are designed to run on Gen. 3.0 but are backwards compatible with PCIe 2.0.
You are limited to using the Nvidia 600 series graphics cards or older Legacy AMD graphics cards.
You may have to upgrade the PSU depending on the graphics card power consumption.
Regards