FINALLY! I got forward from the TI screen to the menu screen:

The above screen I've seen and posted before. I have one button on the FPGA board which emulates TI keyboard button "1". Pushing it used to result in a blank screen, but now I get the following:

So I am moving forward! I started to suspect the system was stuck in GROM discovery loop, and after a quick check with the TI community at Atariage (thank you Tursi!) the symptoms matched. I removed support of the multiple bases for GROMs, and the problem disappeared. But using it again gets me to an empty screen, instead of basic prompt. But this time I have an idea why that happens: I on purpose disabled video interrupts, and I suppose moving from this point on would require interrupts. The reason why I disabled the video interrupts was that the TI gets stuck in the interrupt service routine, in other words the looking at the interrupt line I can see that the system never clears the interrupt request, for one reason or another. That is great progress since this is something I can work on :)