Hey @AKJonathanHolmes; welcome to our Community and sorry to hear you're having issues with deleting files from your account.
Could you check a sample file's version history to see if it's being added back to your account by a linked device of yours or a 3rd party app (or person if this regards shared files or folders) somehow?
If you check the previous versions of the file and see that it was accessed from an application on another computer, you can delete it off of that computer to stop it from reappearing in your Dropbox.
Walter, thanks for the reply. Not sure if I know how to check that, but I did recently get a new computer. Do I need to uninstall Dropbox on my old laptop in order for my new laptop to have authorization to delete files?