Hardware guy, well then it will not be easy. I did some thinking about the problem and knowing that the "I2C" implementation is not to good, there might be a problem with the pull ups being to high. 10K where 2K2 is more usual for I2C. Still a bit weird that after exchanging the "special ic" to the other board left you with two broken boards.
I have to search for the details on the communication between the FPGA and this "special ic" to devise a test you could perform. Others and I did do measurements on it with a saleae logic analyzer clone, so if you have such or a similar device it might shed more light on what is going on.
Maybe it is also possible to hook up the "special ic" to an actual I2C bus connected to a linux machine and see if it responds.
I'm more of a software guy, but with a long ago hardware background, so I know a bit about how things work. Especially not to high frequency digital stuff.