I found this:http://www.tomshardware.com/forum/318839-30-alvorix-rs880-uatx-help
looks like the Motherboard supports up to PCIe 16x v2.0
The 7770 is a PCIe 16x v3.0 card
While it may work it may not work optimally.
A 6850 can be picked up for about the same price ~$100 and is PCIe 16x v2.0
(it is also about the same performance)
The CPU in that machine is somewhat slow however.
(scoring about 1674 avg vs newer CPU scoring 5000+)(cite: passmark)
A complete upgrade might be recommended depending on what you need to do with it.