Well, I'm getting answers all over the place.
This is bonus, so no LCD. Yes, get GUI and can ssh. With or without cubes, same response. I hope its not the controller board. That may prove hard to replace.
The difference is I advocate correctly isolating the problem before throwing money at it if possible.
Based on your response I'd put the BBB last on the list of suspects.
It sounds like you already did all this but lets review.
Unplug everything and start with the simplest possible, just the controller.
Add one cube retest, try a different cube same ribbon cable.
Only change one thing at a time and see if anything works.
Test with the last known locally working version of firmware.
I'd completely unplug the whole controller from everything and let it sit unpowered for a many minutes. I had one I thought I killed. I replaced it with a spare Hoopiter controller. After few reflashes the original came back to life.
This may have been because I had everything unplugged in between flashes and whatever caused the 'lock up' cleared.
(some residual capacitance somewhere in the PCB design that affects the FPGA or the power chip on controller)
The reflashing I did may not have been necessary, the process may just have provided the long enough power down for it to clear.
My priority was getting it back in service so I never properly isolated root cause.
Another thing you can test for.
Take a single cube, unplug the cube power but connect the ribbon.
Turn on the controller and see if the temp on the ASIC shows up on the web page.
The temp chip on the cube is powered by the controller over the ribbon.
If this works the controller is prolly OK, as it tests controller power chip and FPGA operation.
This might/could point to a wierd 12VDC issue on a cube interfering with controller communication.
If/when you think throwing money at it is a good idea...
You might find a used Merc, Sat, or Jup controller with a BBB for what a new BBB would cost.
Those old knc specific BBB lack some connectors and might not be valued as highly seperately FWIW.
YMMV
They only weak point in design of KNC I found was the beagle , espesialy the early versions of the beagle.
A4 , A5 , A6
http://elinux.org/Beagleboard:BeagleBoneBlack here all changes per revision KNC used old BBB I gues they bought a lot of them around 2013/2014/
Now we are at REV C witch is way more robust.
for example a very intresting change is the one from A6 to A6Â
Revision A6A
No changes in features or operation of the board.
1) Added optional zero ohm resistor to tie GND_OSC1 to system ground.
2) Changed C106 to a 1uF capacitor.
3) Changed C24 to a 2.2uF capacitor. This extends the reset signal to solve an issue where some boards would not boot on power up.
4) Removed R9 and installed R8. This change was based on an alert we just received from TI that there is a power sequencing issue with the TPS65217C power management IC and the power sequencing is incorrect. This change connects the VDDS rail to the VRTC rail. We do not believe at this time, that the issue is causing any issues with the boards, but we want to comply
A6A to B
Revision B
This version moves to the AM3358BZCZ100 processor as we are no longer able to get the limited production version of the AM3359AZCZ100.
No changes in features or operation of the board resulted from this change.
Rev B to C
Revision C (Production Version)
This revision increases the eMMC from 2GB to 4GB. We are making this change for several reasons:
1) Complaints from the community about lack of space left in the eMMC.
2) For those worried about their eMMC wearing out, the added space will help in the area of moving the data around to prevent wear out. Assuming of course you don't try and use it all.
3) Concerns over the long-term availability of the 2GB device. 4GB is currently the low end of the offering. This also gives us two sources.
We are planning a price increase for the Rev C somewhere between $5 and $15. We are working to figure out where it needs to be. This is for several reasons:
1) To cover the increased cost of the 4G devices.
2) Currently there is $0 margin on these boards which limits our ability to bring more manufacturing capacity on line. Added some margin allows us to find more capacity.
3) Without margin, we cannot respond to component price increases due to market forces. This is of particular concern in the area of NAND and DDR3. We have been successful in fighting back some increases, but we don't know if that will continue
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The beagle is the center the controlboard acts as a extention to the beagle , and I had it one time that the beagle did not see the cubes , replacing it worked.
s
No surprise that KnC was wrong yet again. 
Still, a Rev B is a cheaper alternative if you can source one and it works just fine. As far as I can see, Rev C just has more onboard memory and some software/GUI improvements that I doubt will matter on a KnC miner.
This is complete BS