Form not responding

Hello all,
I have a quick question. I am looking for some direction here. I have a contact form that I have set up. When I test this form on my server it works perfect. But when I test it on my clients server it doesn’t go through. My client has a site up now that has a contact form and use php just and I am doing, but I am no programmer and I can’t seem to figure out where to start to help me determine what could be going wrong.
Any suggestions would be helpful! Is there something I can trace to see if everything is going through. I just don’t get why it would work on my server but not theirs. Since they have a php form already working on it.

Thanks so much!