I am ready to buy a new video card and It happens to be PCI-E 3.0. my mobo however only has a PCI-E 2.0 slot. My question is will the card still be compatible and just not run at full 3.0 specifications or will it just not run at all?
Yes, it's compatible, any pcie 3.0 gfx card is backwards compatible with previous versions.
Since it's pcie 2.0 at 16x, it will not restrain the card in question.
So you're fine, make sure you have a decent psu with 400-450w.