I can't access my old Backup online, ever since I disable it when preparing to wipe my old laptop.

Hey quackingplums​, thanks for posting here! 

When you try the workaround that you mentioned in order to view your old backup, can you also access the files that way? 

I'm assuming that the backup content isn't visible when you visit your account online either, right? Have you checked your events page to see what it reports? 

One more thing: would you be able to send a couple of screenshots of what you see, in order for us to have a visual too?

Keep in mind that when disabling the feature, there will be a prompt that asks if you want to Keep content in folders on this Mac/PC or Leave content in Dropbox. Do you remember what you checked? 

Let me know more, and we'll take it from there!