The HDD should work, unless it's an ancient kind with an IDE interface (and a wide ribbon-like cable).
If you have already installed Windows and programs on that HDD, they will probably NOT work. Not reliably anyway. The new motherboard wants different drivers than the old one, for example.
What I'd do here: buy an SSD, put it in the new computer, install Windows on it, install the latest drivers for MB and video card, add the old HDD to the new computer, move your documents or saved games or mp3s to the SSD, format the HDD. Don't bother moving programs, just reinstall them after you format.