Code 10s can often be caused by driver incompatibilities - note that just because these are both WDDM1.1 drivers, and the driver model is designed to allow for multiple drivers, is NOT a 100% guarantee of success. That said, while I've never tried these two chipsets together, I would be at least slightly surprised if it was a pure incompatibility based on experience I've had with chipsets of similar vintage.
Code 10s can also be caused by problems allocating resources to the devices - this would be happening on a motherboard level. The most likely cause in this sort of situation would be this: it's possible that there's too much RAM in the machine, including the RAM on the GPUs, for your motherboard to map it all properly (if you can clarify what other hardware is in the machine this would enable me to say this with certainty.) If it is having this trouble, you might find that reducing the amount of RAM installed in the machine would cause the second card to start working. If that's the case, the only solution is replacing the board (or running in the reduced RAM state) but this isn't ideal.
There are also a few other things that could be going on, but they'd all be hardware specific; if you can give some more details I can expound. (One that some budget hardware might have is a limitation on which expansion slots can be active simultaneously at which speeds, but that's unlikely to be an issue with one PCIe and one PCI card.)
Oh, and it should probably go without saying, but - make sure the Radeon 7000 works okay when it's the ONLY card in the machine! If it doesn't, the fact that it's secondary is just a red herring.