If you have a custom theme, you'll also need to make sure it gets copied back into the themes folder or you will get an error when upgrading to v3.
The v2 custom theme you have will kind of work, at least enough for you to go into Administration|Configuration to change the theme to one of the new v3 themes.
I would suggest changing to the default theme before backing up your files and upgrading and then figure out how to modify your custom theme to the new format.