It would appear that your case is a slim one that needs a smaller than ATX psu.
Measure the dimensions of the psu to find out exactly what kind.
I think you might need a TFX psu.
Here is an example; check the dimensions
http://www.newegg.com/Product/Product.aspx?Item=N82E16817151090
A GTX750ti normally does not need any aux 6 pin power and runs entirely on the pcie X16 slot for power.
That is a max of 75w.
Your cpu is a 54w draw, so I think you will be ok.
Be careful to pick a low profile GTX750ti so it will fit in your case.
You could first try without changing the psu.