I have to say I'm not an expert it's just if the conditions have contributed to the grass dying there is no point trying to start a new lot off until things dry out a bit.
would it be better to let the ground dry out a little before sowing the seed? How wet is it? You don't want it to just rot.
Beginning of April it might have a bit more warmth to it too.
Just a thought
It really does look like someone has just skimmed the grass off!