Yup. It can run it, though bandwidth is lil bit limited. That means u cant unleash the full potential of the card, if the card is really powerful like a GTX 260/275 or a 4870/4890.
In worse case, ur mobo wotn detect the card, ull need to update the mobo BIOS to latest. That shud solve the problem.
which is ur mobo?
The bandwidth offered by PCI 1.0a is more than enuf for a 4770.
btw 4770 is no more available. Get a 4850. Prices has really come down.
Check at lynx, sapphire 4850 new one costs 6.5+tax +shipping only. SO total is less than 7k with 3 yrs warranty.