So it's not a server? You are sharing peer to peer using filemaker pro advanced?
Is the new machine using the exact same license key the old one was? (like 100% confirmed)?
I can open the file and have activated the file sharing items on my computer for the file
Do you mean the file sharing in OSX? If so, turn that off! OS-level file sharing is the #1 killer for FM files. Only use the FM native built-in sharing.