I was running a Core i5-2500K (stock speeds) with a Radeon 6670 and three SSDs on 150W in an Antec ISK 300-150 case.

Yes, the 450W PSU that comes with the SG05-450 can power any current single GPU graphics card (that physically fits) and a quad core Intel CPU. Even overclocked. For instance people have shoehorned some of the smaller GTX 680 in there. Those cards use two 6-pin PCIe power plugs that can deliver 75W each, which combined with 75W from the PCIe slot means the card can draw between 150W and 225W. What is the TDP of the CPU?
If you don't believe me, how about a major review site?
Load power consumption - OCCT
Note that this is for the ENTIRE COMPUTER with a quad core CPU, and is for what it pulls from the wall. Here are some examples.
My LAN box (see pic above of ISK 300-150)
Radeon 7750 - 160W
In theory a couple watts less than my 6670
GTX 460 - 270W
Your existing card
My wife's new computer which uses a Silverstone SG05-450
GTX 660 Ti - 290W

The most powerful card you can fit in this case
GTX 680 - 333W
Note that not all will fit, but there are some that do
You should buy a Kill-A-Watt. It will tell you how much power your system is really using (as well as your TV, stereo system, etc). The cheaper model is
currently on sale at Newegg for $17 shipped. It isn't 100% accurate, but should give you a ballpark number.
Note that this doesn't mean you can't use a more powerful PSU. Not all PSUs are able to put out what they claim on the label, plus for the more hardcore overclockers some PSUs get more voltage droop or ripple (anomalies in the power output) as they get near their limit. However, getting two to three times what the system actually needs is kind of a waste of money. Additionally, PSU efficiency usually drops below around 20% of the output. This doesn't mean much at load, but all the times your computer is NOT under load (when you are not benchmarking/torture testing/gaming) then a high wattage PSU can be very inefficient. Web browsing? Watching movies? Messaging/video chat? Yeah, your modern higher end multi-core computer is essentially idling during those times.
Regarding Windows licensing, "officially" the older key still goes with the computer that you put the upgrade on. Will it still work on a second computer? IDK.
Do you live near a Micro Center? You can get the Core i5-2570K bundled with an ASRock Z77E-ITX (IMO the best choice of Z77 ITX motherboard on the market) for $265+tax in-store only. I was able to OC a 3570K (in my wife's computer) to 4.2GHz
undervolted and using a
cheap $16 low profile air cooler. As Ivy Bridge is more powerful at the same MHz as Sandy Bridge, average performance should be near a 2500K @4.4-4.5GHz. So, not necessarily any need for an expensive AIO liquid cooler unless you start adding a lot of voltage and go for higher clocks.
The chipset doesn't have much to do with performance, other than allowing you to use your choice of CPU and GPU as well as overclocking (or not).
Will an i3 game at 1080P? Depends on the game. Most games? Yes. Battlefield 3? Yes, with some settings turned down.