If your htpc has a discrete graphics card, you will find some sort of a model number on it.
You may need to pull the card to inspect it.
If there is no discrete graphics card, find the motherboard make/model.
It may be using the integrated adapter from an intel cpu. The model number of the cpu will lead to the graphics adapter included.
Or, if it is an old or amd motherboard, there may be a graphics adapter chip on the motherboard.
Lastly, there are some utilities that are bootable that will likely tell you all this.