While we can't delete the account from our end, you'll need to regain access to it and delete it. Also, try this guide which has step-by-step recovery instructions: https://goo.gl/dYcTmt . Hope this helps.
Just to confirm, if it's a legacy account, you need to link it to a Google Account to access it. Here's how: https://goo.gl/z8YXdy . Hope this helps.
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Since your old account has been automatically linked to a Brand Account, you need to link that Brand Account to an existing Google Account so you can access your channel. Hope this helps clarify.
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