seeding your lawn with grass

A lot of the grass (st. aug) in my front yard is dead, and there are bare patches for several reasons:
-i let the leaves lie too long on the grass two winters ago, and a bunch of it died
-there are quite a few weeds
-water accumulates in certain areas and it's killed off grass in those spots

can i remedy this by first killing all the weeds and then seeding the yard with new st aug seed? i don't get much sunlight because of all the trees in my yard, so i'm also wondering if i'm going to need to fertilize heavily to help the grass to grow.