Will this power supply fit my HP Pavillion p6774y?

The power supply that you have linked is 6.5" x 3.5" x 6" and the power supply inside your computer is 5.9"x5.5"x3.4" so it is very close and I would say that there is a good chance that it will fit and the case takes an ATX psu so I would look inside your case and see how much extra space is around the psu , it doesn't need much but it would help if there was some.

However this psu is the exact same size as what you now have and is a much better brand name so I would consider this one instead.

http://www.newegg.com/Product/Product.aspx?Item=N82E16817139027

This one is also the same size if you want more watts.

http://www.newegg.com/Product/Product.aspx?Item=N82E16817139028

The video card that you have linked will work and currently you are using intergrated graphics so you have a free pci-e slot for the card.