A black screen + white border is normal for a speccy running its bootup memory test. Its therefore starting to run but is crashing before it does anything useful.
5.77V is too high for the output of a LM2596-5.0, which shoud be in the range 4.8V to 5.2V. It might be a good place to start.
Otherwise its time for a wide logic analyser to trace execution and try to figure out if its crashing predictably. Alternatively as this clone uses SRAM, you might be able to get somewhere with only a logic probe if you build a circuit to assert Z80 /WAIT after N M1 cycles, then allow you to single step the Z80, one M1 cycle at a time.