Personally I'd keep Big Box pre-built computers at a distance...
Your GTX 470's performance is way ahead of the HD 7550, so, I'd give that a pass.
You obviously have a PSU that supports the GTX 470, already have 6GB of RAM, so, frankly it sounds like an upgrade is in order.
Which i3-? i3-5xx use a LGA 1156 socket, and i3-2xxx or i3-3xxx use LGA 1155, so, upgrade choice(s) would depend on that.
Best case is an LGA 1155 mobo with an unlocked(overclockable) BIOS.
With that type of motherboard, the i5-2500K/2550K, i7-2600K/2700K would be great and not require anything else ~$200-$340
A Z68/Z77 chipset LGA 1155 mobo will supply the needed support, if your i3 is in an LGA 1156 socket. ~$125-$150
The only other issue can be the OS. If you need to replace the mobo, and your existing Windows is an OEM version, it may possible to transfer it to an upgraded mobo. If MS won't activate the mobo swap you'll have to grab a new Windows 7(64bit) disk(set). $100oem $180retail
A Mobo, i5-2500K, and Windows will set you back ~$425-450 for a "good" budget upgrade solution.
More for better mobo and/or CPU and/or retail Windows...Don