joy, restarting armory will take another 2 days....
My paper backup only mentions a "root key", this is not the same as a private key.
So I will have to use armory offline to restore the private keys if possible?
No. The private keys are already restored, just that the relevant transactions were not picked up. You can go to the wallet properties and export all off your private keys for that wallet.
Is my balance stored as only 1 private key per wallet or will there be several ?
First of all your balance is not stored in private keys; that's not how Bitcoin works. Secondly, a wallet is a collection of private keys, so there are multiple keys per wallet.