I'm the new owner of a company that had a previous Facebook account, but there's nobody around that knows the username or password of that particular account, and I've already moved on to establish a new Facebook account. Trouble is, the old one is still out there and I want to get rid of it to avoid confusion. How do I do that without any data on the prior account?

You need the user name and password to retrieve it and reactivate it if you wanted to Without a name you can't even look it up

@Young one: Any idea how to get access to user name and password if they're lost forever?

You can deactivate or remove that Facebook account by reporting it to Facebook support or help center.
You need to provide the required details asked for that particular account once you have done it properly that profile will be removed.