Why not just build raised beds there instead? Much easier than trying to salvage that plot, much less expensive, less work, and likely much more productive too.

Dave

I have pretty bad(for digging) clay soil. There is about a 2 week time during spring and fall that we can dig. The rest of the time it is like concrete, or a mud bog!
When we started gardening, we knew we would have to have raised beds.
During our springtime digging window, we forked our areas that we wanted a bed (our first of now 8!), broke it up the best we could, then added a bunch of composted horse manure (from freecycle). Then we built our box and lined it with hardware cloth (gophers) and filled it with an organic mix from a landscape place. We have since discovered that our landfill has an organic mix for half the price!
We also noticed that when we moved our compost bin, the ground was quite digable down to a foot or so!
Now days, with 8 raised beds, we use our own compost and every few years get a truckload of the good stuff trucked in to mix up with my own. The stuff in the raised beds do seem to settle. I have an old 60's mini-tiller that fluffs everything up quite nicely each year!
Happy gardening! Nancy

Since you're in Utah, I suspect that your climate might be similar to here in Idaho. With the dry summers, I have never found drainage to be an issue. On the contrary, with my beds paralleling a slight slope, water will run out under the bed edging quite easily. So what I would do in your situation, is dig down the 4" or so until you hit the compaction layer, and set raised beds in there, and fill them with nice, organic-rich soil, and possibly seed them with earthworms. The compaction layer might actually work in your favor to help retain water in the beds for a longer time in the summer. I just did something similar using 24" tall beds sunk about 6" into the ground and it's working beautifully (I don't have the compaction layer, but I actually put down plastic feed bags to slow the water movement down into the native soil. The taller beds are so nice to work on, and should give your plants enough rooting depth before they hit the compaction layer. Over time, it will probably break up, especially if you plant things with deep, vigorous roots, such as tomatoes. Here is a photo of my beds, which are working out great so far.
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Nancyjane's advice (as well as Dave's and lantanascape's) is great including the hardware cloth for gophers!!!!!!!!!!!!!!!!!!!!!!!

Of course I'm in a similar area with clay soil so that may play a part.

This is exactly my situation. My vegetable garden is on land that used to be a tennis court, and there was clay and gravel fill under it all the way down to China.

First, I trucked in soil to cover it, but that wasn't enough, so I got a tiller and started to till in the vast amounts of chopped leaves from our many trees every fall. Gradually, I've been building up a real soil.

Thanks so much for the answers! Now I don't feel so bad about just building boxes over it. Wow ltilton a tennis court, that can't be good at all. :p

And lantanascape, what kind of metal is that you used? I love that.. looks very clean and nice. Maybe I should do something like that... I'm considering what kind of wood, or other substance, to use for boxes. I am going to cover the weeds with cardboard, read that it really works for killing weeds, then put soil and build boxes over that. I have the book Square Foot Gardner and will follow his plans. I have never done a garden before. My husband used to, but I haven't. I'm including a picture of the beginnings of the garden area. I have to move the pile of bricks to the back of the yard... bleh, such a pain. :)

Not only was the soil bad where we took out the old court, it was of course totally flat, thus poor drainage.

I have not read the Square Foot Gardening book so I will not jump to criticisms but I have read about this 1/3 peat, compost, vermiculite mix for soil. I would personally much rather use organic/'veggie mix' soil from the local landscape supply place than that mix.

Here is a link that might be useful: Local Hero Veggie Mix for example

You will need few days of good rain to soften the soil. OR you keep watering everyday , for a while to make it workable. I have made garden under such situation that even a pick hardly could make a dent. Now that it is the end of season , wait until later in the fall after a lot of rainy days.
Simultaneously I would work in lots of compost, manure, ..

We don't have that kind of problem but I have found it easier to just follow some Lasagna Garden methods of building a raised bed without solid sides. I prefer to have several manageable size beds instead of one big garden. Some people call it sheet composting. The first year when I had time, I kept layering whatever I could to build up a pile about 24 inches tall. In the spring we added composted horse manure that had bedding and kitchen scraps mixed in during the winter. Great craigslist find we have been back to every spring. That original bed built in 2007 in now level with the grass area. It compacts a lot over the first winter. I have tons of earth worms and wonder if you can just let good composting principles and Mother Nature do the work for you. I have friends with salad tables that are quite shallow who brag about how productive they are. After a first hilling of potatoes, I just pile on straw. Here in NH we have trees growing out of crevices in rocks so I bet plant roots and earth worms can eventually make a dent in that solid layer. Also, if you have a raised bed, that should help alleviate drainage problems. You don't have to have solid sides.