Can't get grass to grow -- any tips?

I don't think pictures would help here, I think I can explain it clearly enough without.

My garden has two paths down it that form into a point, so like an inverted V, except it's not a path, it's where there's no grass. I've planted grass seed on it, lots of it, many times, but nothing is coming up. I think it's because:
1. Every day I walk down those two 'paths' to get to my bird bath and bird table.
2. My dog walks down them too.
3. It's clay-based soil and holds water like... well, like plastic.

So what can I do about it? It's getting to be a pain to walk through this thick mud every day. It's so thick that it's pulling my shoes off. On top of that my dog seems not to notice how muddy her paws are and runs into, straight onto the white couch.

 

Clay that feels like plastic and holds the water on the surface says it all to me. I reckon the ground has become so compacted that the grass seed either rots or is eaten by birds before it gets chance to germinate, or it does germinate but can't get its delicate baby roots to penetrate into the compacted clay.

Also, I must ask, you're not trying to grow it at this time of year are you? I assume this is an 'after the event' question following sowing in spring or autumn?

I think the first thing is to aerate it all. Loosen up the clay and get it breathing. Without pics its hard to see where we're at but without seeing it, falling back to my 'default', I'd say a good layer of sharp sand would help loads. It helps with drainage and aeration and provides a nice easy structure for immature grass roots to get established in.

If it is really, really bad (as mine was when I first moved in here), I'd dig the lot over, mix in some bulky organic matter (mushroom compost is good and cheap), level it all off and start again from scratch, but that is a lot of work and unnecessary unless the current lawn is beyond salvage.

 

Get one of these "Roll path"

 

I am talking about past failures (one in summer, another in autumn), but I was about to try again. I was actually told that now is the best time to grow grass. I'm going to guess that it was poor advice...?

 

Yes it was poor advice, seed needs a reasonable temperature and moisture to germinate, turf needs the same to root. As we are only in early January it would be unlikely to get the temperature for seed to germinate and too much of the moisture, If it freezes it could lift any turf and leave unsightly lumps and bumps.

 

The ground needs to consistently be around 10 degrees C for grass seed to germinate. Sow it now and the birds will have it away before it gets chance to germinate. That's if it doesn't rot or simply blow away in the meantime.