What motherboard do you have? If the regular 650ti works on it, then pretty much all PCI-E x16 cards should technically work on it including the boost. I think your problem isn't your motherboard, it is your power supply.
As for returns to newegg, their policy is that if the GPU isn't defective and works you can return it for a refund but you will be charge a re-stocking fee of a certain percentage of the final price of the card plus you will also have to pay for shipping. They may make an exception and let you "trade" it in for a different card plus the difference in price but you would have to ask them. I found this out last year when I bought a Chromebook which I did not like. The restocking fee plus the shipping was just not worth it to me and I put the Chromebook up on ebay and actually got more than I paid for it.
And as for 1GB vs 2GB, you probably won't need that much VRAM with a lower end card like the 650ti since it is probably only capable of playing newer games in 1080p, on one monitor and in medium to medium-high detail. 2GB wouldn't hurt but I don't think it would make much of a difference unless you were doing something with it other than playing video games.