Grass dead? Should I start all over?

Last year I seeded and got decent green grass but I suspect I had lots of weeds or different grass types. The grass became brown last August or so. In preparation for this year, can this be salvaged by throwing seed or fertilizer on top? Or should I till everything down to dirt and re seed?

I am in So-Cal and have no idea when the best time to start. I think last year I started in May or June and probably started too late.