Tried the typical swapping things in/out once more to no avail.
The rest of this post may be boring, just a log of my testing, hopefully may be useful to someone in the future in some way.
I decided to make things more interesting and desoldered the 4 bulged capacitors. I also desoldered a 5th cap of the same type that was nearby.
All 5 of the desoldered caps are TK ATWY 820uF 6.3V.
To test these I will be using a cheap LCR (mega328.) Note that this isn't precision equipment & is for reference only.
Pics w/ captions:
Caps 1-4 fails, returns incomplete test data and measures at ~30 pF.
Cap 5 test doesnt fail and is rather close to spec.
In terms of replacements I'm sure that many choices would work but for this scenario I chose get into the datasheets with the goal of finding the closest replacement possible when it comes to impedance/ripple current. Probably overkill but good chance for me to practice using datasheets etc.
The closest component I could find was a Rubycon "AX" series 820uF, 10v. The Ruby AX has the same impedance of 0.036 and it's rated max ripple current is slightly higher at 1540 compared to the TK ATWY's 1140.
Maybe these failed caps aren't the cause of the board not posting, I don't know their role; if anyone knows what purpose they serve in these particular areas feel free to let me know!
I'll be replacing the 4 bad ones and see if it will post. They arrive in a few days, will update.