/etc folder in basically any Linux / Posix system contains the complete system configuration including basically everything from hardware driver + network config to application software config. Without it and without a backup there is no chance to repair your Linux. Many files here are auto-generated at OS or application software installation time.
To recover the files in
/home/ you have the aready mentioned option to boot the server from a live CD (understood that this does not work for you) or the option to remove the server harddrive and connect it to a different server or PC. You could use e.g. a USB to SATA dongle (if its SATA) to be able to hook up the drive to a running PC. To read the Linux file systems, you will need special tools under Windows or another Linux. You could also boot a linux live CD on your own PC, if that works, and then hook up the drive. To read Linux file systems there is different tools freely available on the web, you could e.g. use TotalCommander with the "Ext2+ Reiser" or the "Ext4" add on (see addons). Be careful not to ruin the filesystems or you may loose all the data (there is always data recovery services available out there, but that will cost a bit). good luck!