I know exactly what you mean! Trying to dig is an "adventure". We ended up getting a few yards of good, amended topsoil and tilled it in. It didn't really cost too awfully much and was an investment that has paid off in spades. We also got a small composter that doesn't take much room and put it next to the house on the south side; it's one of the kind that tumbles..so it processes compost pretty quickly. We got it started with some horse manure.
There's a lady here in Ft Collins who regularly posts on Craig's List: she has rabbits and gives away what manure she can't use...and that's absolutely the best manure there is. It's not "hot" so you can put it directly into the garden, right around the plants.
You can also make raised beds to grow in, adding a little "good" soil, peat moss, compost and such.
Really, I'd encourage you to keep at it...the more stuff you grow, the better the soil will become. The roots will help to break it up and as you till the dead plants back in, they add to it and sort of self compost.
You didn't mention what kind of things you want to grow...is it veggies for yourself, or perhaps some things to supplement your chicken's feed? Root crops in a home garden tend not to do very well unless the soil is amended a lot, ie carrots, beets, potatoes. We can get them to grow, but getting them out of the ground is another story...you pretty much have to dig them out. We do pretty well with tomatoes, green beans, squash, garlic, lettuce, cabbage...stuff like that.
You might consider putting in some alfalfa. It grows really well in our alkaline soil and is a nitrogen fixer as well. You can cut it repeatedly as long as you get it before it sets seed. Then after cutting it'll come back again and again. It is a good food crop for people and excellent for animals. After a year, or less, or more, you can till it all under and it will really help condition the soil as well.
HTH
Mickey