Unfortunately no. You have an older 915g chipset on the motherboard and almost the most powerful processor in that processor family. And unless you have added a graphics card, your integrated Intel video will not be enough either.
The good news is that Gateways are upgradeable unlike some other brands. One of the least expensive and meaningful upgrades I can think of would be the following component. Note: I am using Newegg site for reference as I do not know what your shopping options are. If you cannot buy from Newegg, you can still get part numbers and other useful info from it.
It will still not be a powerful gaming system by today's standard, but it will be way beyond what you have now. You really need a better video card than I have listed, but that is about all your older 300w power supply can handle. Any higher and you would need a new power supply which would be around $50 more for a good quality one.