This error means either that your Bitcoin Core node is not running, or that it has not been configured to accept incoming RPC connections. Armory absolutely relies on Bitcoin Core for receiving transaction
data (from Bitcoin Core block files) and also for creating/sending transactions out to the network (via Bitcoin Core RPC methods)... The data flow would look something like this:
[BITCOIN NETWORK] <---> Bitcoin Core <---> Armory
To allow incoming
RPC connections on Bitcoin Core, you need to start it up using the
-server command line argument when starting bitcoind or put
server=1 in the bitcoin.conf configuration file that lives in the Bitcoin Core data directory (same directory as your wallet.dat file).
Tell me how to transfer my money and I will forget about your wallet.
If your end goal is now to just get your coins out of Armory wallet, you can export your private keys for the addresses that hold coins and then import/sweep them into the wallet of your choice.
I wrote a guide a while ago (with screenshots) that shows how to export private keys from Armory:
https://bitcointalk.org/index.php?topic=2803610.msg30229612#msg30229612