I don't have a dog, but this time of year, a percentage of my grass just looks like that. In the Spring, it all looks lush and green. Since you said you had no real budget for a whole new lawn, I would recommend you wait until next Spring to see what it looks like after a Winter's worth of moisture washing out that doggie burn.

My other recommendation would be to take this picture down to City Floral and ask them for some advice. They have a lot of experience with lawn.

Of course, I'd be tempted to remove it and add some flagstone and flowers. But that's sort of a personal choice.

I would dethatch the lawn and areate ao that the water your putting down actually reaches the roots. Overseeding might not be a bad idea, either.

Second a heavy de-thatch, a double pass at aeration and some overseed. Maybe a top-dress too.

I agree with dethatching and aerating. For information about overseeding, you might check out this story on weed control, which also explains how to overseed a lawn. Denver Post story

Thanks everyone for you comments. Would now be an ok time to dethatch the grass and sprinkle down grass seed and top soil? Or would it be best to wait until next spring?

I guess I should have read the Denver Post story first...

Now is an ideal time because there's less weed competition and more rain than in summer.

It also looks like you are going to have issues with competition from the tree roots for water and nutrients - in my experience, that means you need to use a bit more water and inputs you normally would - but the result is a nice lawn in the shade half the day.

Ok, bought a thatch rake and did some raking this evening. Didn't do too much or too heavily as I only had about 45 minutes to mow, trim and rake. Got 2 kitchen sized trash bags of thatch, grass, leaves, sticks, etc. There are quite a few spots that are just dirt now. I think I'm going to hit it with water pretty good over the next 4-5 days, then pick a spot about 4-5ft square and rake it again. Then areate that spot really well and put down seed and top soil and see what happens. Unless someone has other suggestions...

Here is a photo after first round of dethatching.

Make sure the ground is dry before raking it again.