I recommend that you reinstall and reconfigure any hardware and related drivers, don't copy them over from the old system. If you are copying things that will require you to relink the kernel you are asking for problems because of the differences in hardware between the old and new systems. Do not overwrite any files unless you are sure you need them.
What I usually do for something like this is restore my system backup to a temporary folder I created called "restore", then I pull over the specific files I want, and nothing else. I know this method is slower than a blanket copy, but it's much better than a broken system. If you forget something you can always get it later from the restore folder.
Now I cannot possibly guess everywhere on your system that you may need to pull files for, but here are a few suggestions from my restore notes when I transferred my system to another server. You should be able to do most of this from multiuser mode.
First you will want the auth, passwd and group files from your old system in order to retain your existing users (Be sure to test the root password before you sign off, just in case the encryption has changed and you need to reset it). It may be necessary for passwords to be reset after copying over these, and of course file permissions are also very important.
Next pull over any software source files (i.e. vol files) from your backup that you still need to install, and install them. It may be necessary to reboot after some software installs.
You will also want your hosts file, your init.d files, your gettydefs, your inittab, and ttytype, along with your uucp configurations and printer filters and interfaces, however you will likely have to reinstall the printers before you will get them to work, and if your hardware has changed significantly the port names may be incorrect in the configuration files.
You will then want to pull over any customized script files from the usr folder or other locations, but don't do a blanket copy that overwrites everything or you might dammage critical system files.
Last of all will be your crontabs, and a final reboot to bring your system up live (providing you didn't miss anything)
