Are you using the Beta Patch on SFC III or Out Of Box version?
the Beta Patch fixes collision with enemy ships by making the Borg Cube unable to collide with enemy ships (or friendly ones) but yet keeps it to where it will still collide with bases and astroids and planets.. basically making it act like every other ship in the game...
the Beta Patch also fixes over 150 other game bugs plus gives you the Direct X 9 patch, the Borg Mini Campaign, and the Nemesis Add On all in 1 shot...
if you decide to get the Beta Patch.. First Uninstall SFC III
Delete the SFC III folder out of C:\Program Files\Activision folder
then reinstall SFC III, Patch using Beta Patch only.. do not get any other patches for SFC III or they will corrupt the game...
then try your Borg Cube in a Skirmish against a Starbase and see now it works.. then you can join a Patched D3 server, and / or start over on your single player Conquest Campaign.. only this time, being more lethal...
hope that this information helps