You will have to find out what CPUs the motherboard in that system even support. It's an LGA1155 socket at least, so it *should* be able to support at least Sandy Bridge. May have to contact HP for verification. What games are you trying to stream? If you are trying to stream PC games, I would really recommend going up to 8GB of RAM and a dedicated graphics card as well. If this is for console games the integrated GPU on Sandy Bridge CPUs should be enough. Again, you'll have to find out if there is even a PCI Express slot available for a dedicated GPU, there may not be.
Really though, if you want to be serious about streaming I would recommend saving up for an entirely new system. Pre-built PCs like that are generally a pain to try to upgrade, and tend to lack many features like PCI express slots and CPU support.