I have the exact problem and have been through many onlineHomeShare setup and troubleshooting directions to no avail. I am operating an iMac in Mavericks OS 10.9.3 and iPhone 5 & an iPad both in iOS 7.1.1
I have a large iTune Music Library consisting of 498 GB with 62,000 songs.
I have removed firewalls, verified no ports were blocked, etc., etc.
Any further suggestions will be most welcome.