In general the source code of the restore cd is at GitHub - uroni/urbackup_restore_cd: Builds the UrBackup Restore ISO which allows full system image restores . Releases · uroni/urbackup_restore_cd · GitHub has newer (beta) versions with a <1 year old Linux kernel which should support more recent hardware. Your devices might also be older, so perhaps it works better with older restore cds? Index of /Restore
If possible take a look at the output of dmesg when it doesn’t work. The driver might just be missing a firmware file, which would be relatively easily fixable.
Specifically I210AT, I211 should be supported by Linux Kernel Driver DataBase: CONFIG_IGB: Intel(R) 82575/82576 PCI-Express Gigabit Ethernet support but, yeah, it might just not work in your specific configuration or need fiddling. If possible have a USB ethernet adapter ready (that is known to work reliably – we recently had a thread about that). E.g. Intel and Realtek employees do work to get their drivers upstream (in the official Linux kernel). But sometimes they then forget to update it, or don’t keep up with changes and it rots etc.