InThunderbird:

• Move all mails you want to keep out of the accounts folders to 'Local folders'.
• Go offline.
• Open account settings.
• Mark the account you want to get rid of.
• At the bottom of account-pane there is a button account actions
• Make sure you have the right account marked then Remove account

Only reason to open that account on server would be to clean it up.

What does "I won't be using again" mean?

Simply that you'll never use it to correspond again? Or do you need to retain access to the messages stored in this account?

If there is anything in the account you want to keep, I would, in your position, move this material to folders under Local Folders. Then I'd remove the account from Thunderbird. If you don't, Thunderbird will always want to connect and talk to the server. Yes, you can disable all the automated connecting, but from time to time you will inevitably provoke it into connecting and you'll have the login/password hassle all over again.

Once the retired account is removed from Thunderbird, it won't matter if this account remains on the server or not. But if you remove the account only from the server, you still need to do something about Thunderbird wanting to connect to it, so again, we're back at seeing the need to remove the account from Thunderbird.

So, save the valuable things. Then to remove it, select the account. Right-click it, select Settings. At the bottom of the settings pane, click on Account Actions and remove the account.