I have the private key stored away
The private key is all you need, you can derive the Bitcoin address (and public key) from there if needed.
I have no idea ~ how its stored.
Short answer: on the blockchain
The private key is enough to move funds, but before you do (assuming you want to sell them), make sure you know what you're doing.
Importing the private key into
Electrum is probably the easiest. Depending the amount of Bitcoin you're looking at, you may want to take additional security measures.