OP:
It -might- be the dock hardware, sometimes things just don't work no matter what you try.
Is the dock a "single bay" dock, or does it have "dual" bays?
If you connect the drives and dock to a DIFFERENT Mac, running an older version of the OS, do they mount on the desktop "as normally expected"?
When you connect the dock in question, DO YOU HAVE ANY OTHER HARDWARE connected to your USB ports? I know this sounds strange, but I've had experiences where if I tried to connect two USB drives/docks at once, things went fuzzy...
Are you connecting directly to the USB port on the back of the Mac, or is there a hub "in between"?
Have you opened System Information and checked the "USB" info?
Does it show the presence of the Startech dock/controller chip?
At the very least, have you tried a different USB connecting cable?
Is there any way to boot the Mac into the older version of the OS, so you can verify that the dock is still working with it?
Various USB enclosures and docks (and dongles) use different USB controller chips.
It's -possible- that the chip in the Startech is somehow being "overlooked" by the Yosemite OS.
It might be possible to get another dock which WILL be recognized by Yosemite, and then you'll be back to normal.
Have you tried Startech tech support (not Apple)?
Do they have any kind of tech support boards?
You need to get some paper and start taking notes.