My guess based on the blank page (white screen of death) that you are getting is one of two things. The first is not very likely; duplicate PHP function names or a missing required function. The second, the memory assigned to PHP is being exhausted. I suggest trying to increase that memory allocation. Here’s an excellent article that outlines how to do this. Which method will work will depend on your web host. I suggest starting at the top on working you way down.
All known plugin and theme conflicts can be found on this page. AS far as I know, Avanda and Connections work just fine together as I have helped others using that theme and there was no conflicts with it in their setup.
Let me know if that helps.