I usually use git and know little beyond the basics of Subversion, so please be gentle.
I'm using TortoiseSVN on Windows 7. The SVN client recently announced it needed to upgrade, so I did that. All files lost their source control icons, and a new menu item appeared in Explorer prompting me to upgrade my repository working copy to v1.7. I did that and see the error attached.
I've searched for the file it mentions, it does not exist in my local repository. I seem unable to do a Clean as the menu item doesn't exist as the TortoiseSVN menu has reduced to bare basics: Repo browser (which opens an empty dialog), Properties, Settings, Help, About.
What complicates matters is I have local changes, so I can't trash my local copy and update my local from the repository.
How can I fix my broken local copy, whilst maintaining my local changes?
Your working copy needs to be updated which means in other words simply make a fresh checkout with the new installed TortoiseSVN client (1.7.x) instead of using the old working copy. The repository doesn't need an update (you can if you like). The simplest solution is to create a fresh checkout into a different directory and then copy your changes to that new working copy and do a commit from there. Why did you do an update without prior checking in all recent changes?
The message says:
Try a 'Cleanup'. If that doesn't work you need to do a fresh checkout.
So what I would do is try a cleanup. And if it didn't work, I would do a fresh checkout.
These two commands are in the TortoiseSVN context menu. And there's also a Help menu if yo don't understand how these commands work.
If you end up doing a fresh checkout, you can always use WinMerge to compare your old, corrupted working copy with the new one, and reapply your local changes to your fresh working copy.