Hi Kara,
you will definitly give a chance to your lawn by mowing it higher. You should consider seeding in your backyard and choose seeds that are made especially for shaded areas. It might be a good idea to aerate your lawn before seeding, it'll be a good think for root development. I know you mentioned you didn't want to spend money on it, but fertilizing will help your lawn stay healthy and again will help roots.
If you need more infos, you might want to consider reading a few posts on mowing your lawn, fertilizing and overseeding here: www.thegreengrass.ca
Hope it helps a bit!
Have a good one!
