Fixing Wordress log on – emergency

I had trouble migrating a wordpress installation in a lower folder of my site to the top level. I contacted tech support of my hosting provider and it was a big mistake. They did a series of administrative changes to point the url toward the lower folder, but in the process they messed some things up, like my plugins, but most important the wordpress sign on is broken so I can’t log on. They’re now telling me that in order to fix that I may lose all my theme settings. They asked me for permission to go ahead. Obviously, I told them no.
Is there any way to fix the log on?

I’m at my wits end. This is months of work being destroyed.

The page I need help with: [log in to see the link]