Well I think the 400w will work but we need to know the brand who makes it or what does the sticker on the side show what is on the 12v rail 3.3 .5 etc. If there is enough amp on the 12v rail then you can use the 400w PSU.
AMD web site show a 450w for the 6770 but if your PSU is good you won't have to worry about it. Here is the link to AMD site.
The 7750 uses about 51w on load as the 6670 uses a lot more but your PSU will run both cards. On the last link go to the last chart. It is in German. It is set up like ours is. First chart Idel, Med, and Peak.