Hi,
Firstly, could you add the snippets a bit close-up ? It's really hard to see the details, therefore to debug. Regarding the issues:
1) If the Tick_FPGA is staying low, your FSM might be stuck at the IDLE state, waiting for Dio_tick. In the second snippet I see that there's a rapid transition of Dio_tick to 0 and then back to 1, maybe this transition happens when the FSM is not in the IDLE state but in another state. But since there's no state signal in the waveforms, I cannot be sure. Maybe you can add that one and the counter signals to the waveform ?
2) What is DATA in A4 ? data_in or data_out ? If it's data_in, it could be the same as 1), getting the data_valid transition to 0 in another state. But if it's data_out, it should be stuck in the BUSY_1 state indeed, but that shouldn't be the case given that the data_valid is wide enough for the clock to catch.
My idea is that you're stuck at the reset state for the most of the time, and when it's out of that, the FSM barely has time to do anything (I assume A4 is data_in)