That's not the problem. Mine along with millions of others work with iCloud sync.
Check these options:
1) make sure your computer and iPhone really are on the same network. If there's a nearby wifi network that you've already gotten on, it may mistakenly pick that up instead of your home network.
2) with your iPhone plugged in, make sure sync over wifi is checked on the summary page AND sync automatically when connected to iTunes is checked. THEN hit apply and disconnect your iPhone.
3) make sure your computer and iDevices are logged into the same iTunes account
4) make sure your iPhone shows up in the sidebar in iTunes like its connected manually. If not, restart your computer. Just Restarting iTunes doesn't work when your iPhone fails to show up in the sidebar or if you get an error message.
5) if all of that fails, try restoring from a backup to see if that does anything. And if that fails, sounds like a trip to the Genius Bar is in your future.
I'm not a network guy but I've seen some instances in here where the router is the problem. There may be some settings you can check. Maybe someone more network savvy can chime in.