Its no use sending samples to Goy Mavis, this is just a blogging site - there are may experts among the members but nowhere central to send samples to. If you could attach some close up photographs to your question hopefully someone who knows a lot about lawns will be able to advise you. Without a picture its pointless to take even a wild guess.
The most likely thing in a wet area is either moss or some sort of rush or perhaps a liverwort. If you can't attach a pic to this question just ask it again from the beginning - you'll see an option for adding one.

Uh...first time I have ever heard of sending snail mail to an email address. They must have been scratching their heads over this at the P.O.

Wet and soggy and north facing does sound like moss and liverworts have taken over the grass. To be honest I think you are best without grass. Does the moss/liverwort offend you? Even if you improve drainage the lack of sun all year round, esp during winter, does not lend itself to a grass lawn so you should look for the right plant for the right place.

Might be moss or liverwort, but might also be algae or slime mould, without a photo, can't say.

It would also be good to have a photo of the area generally - perhaps its possible to remove the grass there and have some planting instead, which would look better in winter. Having had a north facing garden myself, certainly the lawn nearer the house got very muddy and mucky in winter, but it was a good 6/8 feet from the back door, and always recovered and looked fine once summer arrived. If your lawn is very close to the house, but not near a door or where you need to walk, it might be possible to do a bit of shade planting instead.

I'm with Botanic and Bamboo. Trying to grow a lawn on that site is going to be hard work. in my last garden I took up the lawn on the north side and laid a weed proof membrane with bark chippings over the top. Then I cut holes in the membrane and planted shade tolerant plants like ferns and Hostas etc. all white flowers. It worked a treat and looked beautiful all year around. Also much less to maintain than a lawn. :) doing exactly the same here in my new garden but sadly no membrane, so a lot more weeding required! :)