My /etc/rc*.d have disappeared, and now apt-get install doesn't work.
Is this normal? How to fix it?
It doesn't sound normal at all. You may need to either restore from a recent backup, if you have one, or do a lot of work to actually fix things. If those files are actually gone, then other things are probably broken as well, you may need to completely rebuild the system.
I would suggest trying to boot off a live-cd and see if you can see your files.