I think it depends a lot on your climate and soil. If you live somewhere temperate like near the coast in Washington where blackberries commonly grow wild, I'm guessing they'll grow like weeds right away. I could be wrong about them growing like weeds right away in those areas, but that's the impression I get.
In my garden, which has a more clay-type soil, lots of summer heat, lots of sun, and a semi-arid climate, blackberries are prone to looking stunted for the first year or two after the transplant, and then they take off and grow plenty of fruit thereafter. It seems like it takes them a while to get used to the heat, the semi-ardidity, and/or the clay-type soil—but, get used to it they do. They can be hard to get rid of once they're established.
I doubt your blackberries are dead, especially if they look healthy, although it is possible. Transplant success rates with blackberries aren't 100%, from what I've seen.
You might try looking for more heat tolerant varieties, which possibly might be less likely to be stunted in heat the first couple years. I've heard of a couple varieties that do particularly well in the heat.
I'm not sure what southwestern Pennsylvania is like with heat, but the clay in the soil might be the issue if the heat and drought aren't (sounds like drought isn't the issue). Like others, though, I do recommend a soil test. We haven't had ours tested, yet; so, it could just have pH issues or something. However, if you're patient, you can likely still grow blackberries in it without doing anything too special.
I can tell you that there does seem to be zinc deficiency in at least some of our soil, though. Zinc deficiency can stunt plants, as can other deficiencies.