My guess is that you've got a damaged FPGA. There's a path from the 3.3V IO power to the 1.2V core power.6
You could test this the other way around: disconnect the regulators and power the 3.3V and 1.2V from power supplies and see what happens; I don't think you can do any more damage than has already occurred.
Is it possible something external to the FPGA failed-you don't show us much of a schematic? Could you have had ESD damage? A floating blob of solder?