After another weekend on fumbling on why the ASTB that wasn't strobing, I had to take apart the FPGA and the V20, and did some research on it. 

Referring to the page: http://www.vcfed.org/forum/showthread.php?53999-Suspected-fake-counterfeit-NEC-V20-uPD70108HCZ, seems that to get the ASTB to strobe, I had to connect this to a 74LS245. The other port of the 74LS245 is a bit pattern 0b10010000 (x86 NOP instruction). Without the ASTB strobing, the rest of it will not work even if I connect the FPGA to it (this schematic is made using EasyEDA):

With all the trial-and-error again, I breadboarded everything and connected the clock to the Analog DIscovery 2's waveform generator. Also, the supply is +3.3V because I wanted it to be compatible with the FPGA board.

And there's the ASTB strobing! Unfortunately, the noise was terrible and I'm planning to get rid of it as much as possible!

Well, it's at least working, but the challenge is to put this back into that FPGA! No easy task, I'm expecting a lot of roadblocks ahead! :)