Don't remove or modify the original theme while doing the upgrade. Install the new theme you want to work on and switch to it for testing. Then you can switch back to the old theme when you're done and still have a functioning website.
Apparently, the new theme has a whole different configuration from my current theme, and I have to set up the whole site differently. My homepage became "This is a Wordpress post. To edit this ..."
And I have to go through the individual posts again to reconfigure the photos, etc.
I'll change the theme, but only when I have the time to really work on it nonstop because it seems that I have to reconfigure the whole thing -- homepage, sidebars, design, etc. So I reverted back to my old theme in the meantime