Basic theme isn't working any more

I uploaded a new favicon and header icon to the site, and it stopped the default ‘Bartik’ theme from working any more. With it still installed as default, my site now looks like this:

Only local images are allowed.

Any time I try to change theme or edit any part of the appearance, I get page not found or access denied errors. Is there any way of fixing this short of deleting the whole install and starting over?

Also, how do I put a picture on here, the put picture option doesn’t do anything?