You don't need to spend 80 dollars on a new PSU for a GTX 560 Ti.
I doubt a 350w PSU of even good quality would run it. Even if its of good quaulity and it works, you'll be pushing the PSU to the limit create heat and just putting a lot of stress on the system.
If you want something cheap go for something like a Corsair 500w, I think they are like 50 dollars after rebate right now.
Guru 3D says the system takes 319w with a GTX 560 Ti
System Wattage with GPU in FULL Stress = 319W
So yeah, no you need a new PSU
Here is a few good PSUs that will run a GTX 560 Ti and aren't super expensive.http://www.newegg.com/Product/Product.aspx?Item=N82E16817139027http://www.newegg.com/Product/Product.aspx?Item=N82E16817256061http://www.newegg.com/Product/Product.aspx?Item=N82E16817341016