That shop should close up doors NOW. for real, I used a 5770 on a core2 system with DDR2. It even had an older board then yours.
Video memory does NOT need to match motherboard memory.
After all, motherboards only go upto DDR3
As long as your power supply meets the requirements(AMD says 450, you can get by with less if it is a good quality unit), you are good to go.
@ cliffro, I get a good laugh every time I see your avatar/quote