At that price you are pushing the boundary of gaming pc's. You probably won't be able to get a quad core and a dedicated graphics card unless you look at older models. That pc should run those games, however, at low to medium graphics. If you want more than that it is probably worth waiting for a little longer so you can spend a bit more and get a slightly more powerful pc.
Your OS may be an issue - did you buy the pc with windows pre installed? If so then the install may be tied to that computer meaning you will need to purchase a new OS.
Here is a quote from HowToGeek to explain:
"Never Allowed: Moving a preinstalled licence to a new pc
When you get a computer that comes with Windows system preinstalled by the manufacturer, the Windows license will always remain tied to that computer. There’s no exception to this, aside from the exception for replacing the computer’s motherboard if it failed, as discussed above. Manufacturers get these non-transferable licences for less than you’d pay for a transferable license, hence the restriction."
Moving the hard drive across might work in respect to licensing, though I am very doubtful, and you may have driver mayhem for a little while!
Let me know if you have any other questions!