Ah, sorry for the confusion. My first thought was you're trying to restore it so I wondered why you need to switch themes. Then my second thought was just you're just starting from scratch due to HTML issues.
I recommend consulting it to a webmaster or developer as the process of moving and fixing HTML issues are complex. I can't provide any instructions as I'm not sure what to fix on your site.
Though, I still just recommend restoring your site to when the widgets are still working then just delete the current X theme and install it again in Admin > Themes > Add New > Upload Theme. Then check the widgets and re-add them again.