The ratchets, or binding clips, on your bindings are generally reliable, but most snowboarders experience a stuck or broken ratchet at some point. If your ratchet gets stuck when you strap in, it's likely that something is stuck inside the ratchet or you are fastening it down too tight. If pieces of your ratchet are broken off, there's no way to repair it. Fortunately these straps are inexpensive and available at any snowboard shop.
Chip away at any ice or snow stuck inside the ratchet with your snowboard tool. Pull the ratchet up and make sure it is clear before trying to tighten it. Leave a few ratchet spaces on the end when you tighten the ratchet down over your boot. If you can't get the ratchet loose when tightened on your boot, you have probably tightened it too far.
Remove the strap where it meets the base of your binding if the ratchet clip has completely broken off, or if chipping away the ice or snow doesn't repair it. Most binding straps can be removed with an Allen wrench, but some companies use Phillips head screws.
Buy a new padded ratchet strap from the tech center or snowboard shop. They may even give you a spare strap they have lying around for free. Screw the new ratchet strap into place where you removed the broken one and get back on the mountain.