Have to hold down power button to turn off. When I powered back up, gets stuck in reboot

First step would be to repair your disk and permissions fromm the OS DVD supplied with the computer on the Air you will need a USB DVD player or a Mac that will allow drive sharing. Before starting the install open the tools menue and run disk utility select the Hard Drive and under the First-aid screen run disk repait and permissions repait if this dose not fix it try a reinstall of the OS.