Hey Mary-
First off, you need to let the ground thaw out.
As was mentioned, you are using the incorrect shovel. A spade is what you need, and a mattock works wonders for busting up hard soil. Matlock was the Perry Mason knockoff. I would say though, that you might have a bit of an issue using a mattock, so...
However, the small size of your yard and the hard soil makes your spot a perfect candidate for raised beds, as I mentioned to you several months ago. If you have an issue with tree roots, particularly maples, they are going to love soft garden soil, so line it with landscaping fabric to help hold them back.
If you don't want to go the raised route, then getting someone with a tiller will be the way to go. I'm sure someone nearby has one, if you slip them a few bucks.