Unfortunately there is no simple formula to determine if a specific plugin and theme will work together. There is no testing body that mixes all possible combinations together to verify the work; there are too many themes and plugins for such a solution to be viable.
This leaves the ownership of the task in the hands of those that are trying to install the pieces together. Since you have a paid theme it presumably means you have support for that theme. If you haven't already, contact the theme maker with your issue for assistance. If it broke all plugins, chances are there is a problem in the theme. You could also go to the support pages for the plugins to post a question about the compatibility problem you see.
One thing to try before going for help though is to confirm which plugins are broken. I assume first that they work without your new theme. Enable the new theme and then start turning them on one by one with the new theme and test. When one breaks, make note, disable and try another of your plugins. Once you have your list, contact the theme builder and plugin developers for more assistance in resolving the conflict.