Those HP's and many others require the board to have the makers "TATTOO" and no shop I know does this.
With that said, even if you got the motherboard for free your installed OS will not boot. It will notice it's not a HP board and then fail. Why this is often the end of that PC is that once you factor in the cost of a new OS and how most folk are not willing to learn how to install Windows (you can tell it when they ask how?) I fear the best deal is to let HP give you a quote and then decide.
We have a HPE-150t desktop computer. We need to replace the motherboard. I guess it would be easiest to just replace with the same one. So, where would I buy an MS-7613 (Iona-GL8E) motherboard that would have a warranty with it?