Are you sure that the bootloader has a built-in RAM test? Never heard of this before...
Still, the bootloader uses the upper RAM for its stack and variables (0xe000-0xffff). Coincidentally, this is also the upper bank of the video frame buffer - the only one used by the bootloader in order to reserve all RAM below 0xe000 for loading programs (hence the pixel "garbage" in the upper right corner of the bootloader grid screen)
So if the corresponding memory chips are corrupted or do not receive proper signals, neither the grid will be visible nor the bootloader will be able to operate normally.
Also, it's strange that you can hear signal coming to the tape input from the speaker. I cannot recall this being the case, as the tape input should go directly to the comparator circuitry.
I would double-check if you are not mistakenly using tape out instead of tape in.
Could be a quirk of the early motherboard revision you have, though.





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