ice40-hx8k: Weird input pin behaviour regarding digital HI voltage level
Taking all evidence into consideration the assumption that the board (or IO bank) is broken (to some extend) seems valid. 

Reasoning: It is unlikely to be a settings thing as it works as expected on the other I/O banks. The fact 3.3V is required to trigger the input is an indication that VCCIO of the bank is connected to 3.3V so it is unlikely to be a faulty or missing connection/jumper (For the MachXO3LF FPGAS I observed that current consumption over VCORE goes high if the VCCIO are not supplied correctly - maybe an indication that 1.2V is then flowing through the IO bank).

But without another board to verify this there is still a slim chance that it is something different of course.