Unbelievably stubborn lack of COM port

I've sort of run out of ideas, have been troubleshooting this for 2 days at work. I have 3 different Arduino Megas that I have connected to three different laptops with two different cables in pretty much every permutation I can come up with. The boards never show up in device manager or the ide. I have tried uninstalling the ide and reinstalling it multiple times on every computer, I tried hdwwiz.exe to try to force an install but that generates an installation that seems to not be genuine (generates an unresolvable code 10 error). I also tried everything via ICSP and I can't get that to work either.

The one board with a sketch on it runs that sketch successfully with power.

I'm at a loss, thanks in advance for any help y'all can give.

EDIT:
I should mention they are Mega2560 boards sitting on an esd mat with nothing connected to it other than a USB or ICSP cable.

Examine the markings on the black IC near the USB port. What is it?

If it's an Atmel 16u2, the official driver should work.

If it's something else (CH340G, CP2102, FT232), it's a clone with a different serial chip, google that part number, your operating system, and the word "drivers", download and install.

annoyedferret:
I also tried everything via ICSP and I can't get that to work either.

This comment doesn't make sense. What do you mean "everything via ICSP"? What programmer are you using? Since ICSP programming is completely different than serial programming, what was the difference in error messages?

Same/similar problem: Win7 or Win10 Port in Arduino IDE 1.6.4 or1.83 shows port grayed out.
Loaded all drivers for Trinket etc can not get a port to show up.
Bottom line in IDE says: "Adafruit Trinket 8MHz on COM1" but won't let me select a port and complains that no port is selected.
Reset on Trinket tries to load a driver and I get "USB Not Recognized"
I've spent 3 days on this!

On windows the port is very doubtful to be COM 1.
What does device manager in either win 7 or 10 show in the COM ports or unknown devices.
(include a screen shot if possible)

Note that on win 10 and possibly win 7 you may need to install drivers as ADMINISTRATOR which is different from a user with admin rights.
Turning off driver signing may also be needed depending on your user level on those computers.
All of which is easily googled.