An e8400 + 7770 (+other standard components) would pull around 200W max theoretical load.....
A good quality 400W PSU should be sufficient, but it'll depend on the make/model & age of the PSU.
I believe a 7770 requires 12a on the 12V rail, so it sounds ok - but if you have a PSU will misleading specs etc, or that's particularly old/deteriorating, it may be an issue.