No, but there's no way to know if you don't have a good PSU. You need to start somewhere when troubleshooting, and the first step is having parts that will work together. A low wattage PSU and a 5870 won't work together.
That said, I'm fairly certain it's not the board. You said everything works fine when you remove the GPU. That indicates that the problem is most likely to be either the GPU or the PSU. Those are the only items that cause further stress to the system when the GPU is added. It's possible that the PCIe 2.0 slot is defective, but it's not likely. If this were the case, the build wouldn't be likely to work even without the GPU.