So, I have moved the .bitcoin folder to another computer on my home network, but when I run the
"bitcoin-qt -datadir=/home/*******/BITCOIN/.bitcoin"
from the command line, it launches but opens with an empty wallet, and recreates a new .bitcoin folder in my old Home partition, and starts to redownload from the internet.
You're not very clear. You're talking about moving your data to an other computer. Are you trying to use NFS or something? I doubt so. I suspect you're talking about mounting your .bitcoin directory on an other partition. Which is the simplest solution to your problem. If you do so, you can also use symbolic links to store your wallet somewhere else.
Also, it might be necessary to define the new location for your datadir in bitcoin.conf (which must be present in both destination, I guess). Though just on command line should be enough, normally.
