I'm hoping someone can help me with this, because I've been trying to troubleshoot it on my own for a few weeks on and off with no luck.

WHAT I'VE TRIED:
(1) Examined my soldering under magnification (multiple times). No shorts and no bad joints found.
(2) Re-soldered three of the chips that I suspected just in case. No change.
(3) Re-examined the installation of all IC's for orientation or wrong-socket issues. No issues found.
(4) Burned multiple copies of multiple versions of the ROM into different EPROM's (Ver. 5a, 4, and 3) and tried them all. No change.
(5) Removed all chips (socketed) and tested all TTL chips in my EPROM burner / TTL tester. All show as good. Re-installed: No change.
(6) Examined the installation of all non-IC components twice (including the only TO-92 component). All appear to be correct in both component value and direction (where it matters).
(7) Examined board according to the "Troubleshooting" Excel spreadsheet. Results:
(a) According to "Diode Mode" check page, all values are within 100mV of nominal. Most non-zero values are off by 100mV, but if I understand the directions, this is good enough. All nominal-zero values are very, very near zero.
(b) According to the "Voltage Mode" check page, several things are wrong:
(i) U1 pins 5 & 8 are 1.96V instead of 2.5V
(ii) U3 pin 11 is 5.0V instead of 2.4V, pin 14 is 3.7V instead of 2.8. Others are close.
(iii) U4 pins 11-14 are all wrong.
(iv) U14 most of the yellow-highlighted pins are wrong.
(v) U39 yellow-highlighted pins all wrong.
(8) Connected my Arduino Uno to the board according to the instructions in that test sketch (linked from another forum thread). Found a strange issue with the instructions where they skipped Arduino Pin 12 but used Pin 13 twice, without mentioning that this was intentional. As one use of Pin 13 was as a "probe" line and the other wasn't, I made the (unwarranted?) assumption that the first mention of pin 13 was intended to be Pin 12. Proceeding thusly:
(a) First Test:
The Blinkenlights don't seem so "odd and even sequentially" to me.
U7 (ROM - Removed): Not sure about pins 35-37; others fine
U11: Fine
U13: Fine
U14: Pins 3 and 13 don't blink the indicator
U10: Fine
(b) Second Test:
All fine, I think
(c) Third Test:
U20: Fine
U30: Fine
U31: Doesn't match pattern of 5, 9, 12, 16 on while 2, 6, 15, 29 are off
U36 (RAM): Fine except for Pin 27 (doesn't blink)
(d) Fourth Test:
U37: Pin 19 doesn't blink; others fine
(e) Fifth Test:
With controller: Complete failure; but, is my controller even correct? The controller on the parts list is no longer available (at least, not from the included link), so I didn't get one. I do have a 9-pin Famicom controller that came with a modern Famicom work-alike clone, though, so I tried that, hoping it had the expected pinout. However, I do not know this for sure.
Trying with Pluggy McPlugface: No response.
(f) Next tests:
Not sure they did anything? Testing instructions, but no feedback except on LD, and it didn't make much sense.
(9) I went over the whole board with my multimeter in connectivity mode, looking for shorts between adjacent pins, but I found none.
SUMMARY: I have tested everything in every way I can think of or find online, and I cannot find any reason that this build will not work; yet it stubbornly refuses to do so! I've successfully built about twenty other hobbyist computer kits (some complete kits; others a board design an Bill of Materials), so I'm not completely new to soldering or even to complex soldering projects. I say that not to brag, but just to make it clear that I "should" know what I'm doing, BUT I'm fully willing to believe that I've screwed up in some way here; I just can't find it!
What should I test or otherwise do next?
Thank you in advance to anyone who can help me find the problem(s) with my Gigatron build!

-Derek