I don't believe you'll be able to get network connectivity while booted from the normal install DVD. The simplest approach is indeed JRobert's answer of FireWire Target Disk Mode, but if you absolutely need to do it over a network, it is possible to create a custom bootable install of OS X with network connectivity that could be burned to a DVD (or flash drive, even).
Of course, for my time, I'd rather extract the hard drive and back it up connected to an external interface... assuming you've got one of the white iMacs and not an aluminum.
Ah, better answer: boot from the install DVD you have, run Disk Utility, and then image your broken drive to an external hard drive.
And lastly, if you can boot successfully into safe mode, it may be possible to fix your install from the command line assuming you know what's broken.