I assume that the vulnerability of the ROM is not very important, because of the following:
...quote from opening post...
Which leads me to believe that every version is rootable (I have an old CC stick). I believe the problem is the HDD connector, because it either is not capable of connecting because there is a resistor inside of it or it is one way as it is normally used for connecting the HDD to a hub with two USB ports so it can start properly.
So check the Chromecast app to see what build your Chromecast has. If it is 19084 or greater, it cannot be rooted nor can it be downgraded since flashing requires exploitable bootloader (such it's also what root requires).
See my signature for more info.