I have 10.6.4 and when I try to update my computer it says "The Software Update Server (Server.local) is not responding."

You can download and install the update from the Apple Support Page, see the link below:

http://support.apple.com/kb/DL1399

Then try running software update again and see if you can connect to Software Update.

The error sounds like your machine has had its update server changed to point to a local SUS on the domain Server.local

try this

defaults delete /Library/Preferences/com.apple.SoftwareUpdate CatalogURL

taken from

http://support.apple.com/kb/HT4069?viewlocale=en_US&locale=en_US