Problem is most likely due to a Javascript conflict with either your current WordPress theme or one of the other plugins you are using - see Solving CF7 Javascript Conflicts.
The spinning arrow is a common symptom.
There are so many poorly written themes and plugins that cause Javascript conflicts with well written plugins like CF7. You have my sympathy.
Mostly due to not enqueing Javascript correctly, which is poor coding practice that creates a strong risk of conflicting with other themes and plugins - see http://wp.tutsplus.com/articles/how-to-include-javascript-and-css-in-your-wordpress-themes-and-plugins/
Remember that a problem in one script can cause issues in another. For example, some jQuery errors can stop jQuery processing any more script, which can make the culprit hard to find. A jQuery error in one of your plugins or your themes javascript files can stop jQuery processing before it gets to the CF7 script.
Use Firebug or Chrome Dev Tools to examine Javascript conflicts in detail - see Use Firebug or Chrome Dev Tools.
You will need to be skilled at using Firebug to find what is causing your Javascript conflict and how to resolve it - see https://getfirebug.com/wiki/