hi,unfortunately, the new ipod devices required the latest itunes software to sync because latest itunes have driver support your new ipod classic.new itunes required faster computer and the latest osx operating system.there are no workaround method for it. you have to buy a new computer or find another computer in your house and install itunes in there.
great news go here and download itunes 9 for mac ---->>> http://tinyurl.com/mqs59t
try to download itunes 9 and install it
then sync your ipod classic again
as a reminder using old itunes with new ipod classic. you might encounter some bugs
but give it a try