Can I save this lawn or should I lay new sod?

[Habs4life]

Hi first I would like to say my name is Matt and I'm new to this forum. I live in Windsor Ontario which borders Detroit Michigan. I guess my first question will be is my grass a cool season grass or warm season? I think it's cool but would appreciate confirmation on that.
Here's my dilema I just bought a brand new home which was built about a year ago. The builder had sod put in the front and back but at this point it looks real bad. Best way to describe it is a light brown color with quite a few bare spots. Also we've had quite a bit of rain lately and when I walk on it it is very soggy. The builder did waranty the sod, but I said I would do what I could to get it back. If I keep it what I have planned is to have it aerated and then overseed it and put down a fertilizer, I was thinking starter fertilizer? From there maintain it properly with water, mowing and regular fertilizing and probably overseed again in the fall. Problem is I can't distinguish if the sod is dead or just dormant at this point. If it's dead I would rather not waste all that money on paying to have it aerated and so on.
So....if you think I should re sod I have a few questions. Can I just spray round up and let it sit till the existing sod is dead then rent a tiller and till the existing sod or does it need to be scalped or cut and taken away? The place I get my sod from says 100% Kentucky Bluegrass. I hear it's better to have a mix with fescue and rye grass, is that true. Also I have some shaded areas in my back and I heard KB does best in sunlight. If I did go with KB would it be sufficient to overseed with a mix of KB, fescue and rye grass in the fall?
What do you think? can I save this sod or do I need to go with new sod. Any tips or advice would be greatly appreciated,
Thanks.