Or do I have to erase and install and lose all the data.
Even if you end up having to reinstall the OS from the little USB drive that came with the Air, it shouldn't erase your data.
Starting with Snow Leopard (10.6), if you want to erase your HDD before doing an OS install, you manually have to go into Disk Utility and format the disk yourself.
Your other option is to try to install OS X on an external USB drive and boot off of that. Once rebooted, you should see your internal drive and be able to copy data off of it.
But like Intell said, booting in safe mode will probably fix the issue you're having. And if not, reinstalling the OS shouldn't wipe your user data, assuming you're installing Snow Leopard. If you have an older Air and are installing Leopard, you just have to be sure to check "Archive and Install" as your custom option. (Snow Leopard does that by default)