That combo will be ok for most games, but you will not be able to play the latest games at high settings. The PSU might be something to look at, as from what I can see, it may be unreliable. Also with the new AMD APU's they like to have speedy RAM and the RAM on there is 1333MHz which might not be amazing. Although looking at your old PC it is definatly time to upgrade if you want to play games.
I will be taking apart my old PC and using the old hard drive for back up and I have a optical rive in there. I was hoping I could use the Win 7 from the old computer but I do not know if it would work.
also i refined the new Pc a little bit. http://pcpartpicker.com/p/zFxE
I did a little bit and I came to the conclusion that for a discrete video card it would be about 100 more dollars for the same experience and I don't think I would have that kind of money. If you would like to offer some advice on helping this system be my guest.
I found a video on youtube with someone using a a10-5800k on bf3 and this person shows you the sepcs they play at, so I will link that below. As far as the build goes the ram is nice and fast and should perform well. It always throws me off how they call it intel extreme, but oh well.
No I believe the hd 6670 is the highest card you can hybrid crossfire with. If you are happy with the settings on the bf3 video you don't need a hd 6670 anyway. Also see if you can get someone elses opinion too. Even though I'm more than happy to help having two people look at it from different perspectives can always help.