Our shredder is a Kobra 240 ss5. It will turn backward but not forward. The circuit board has a burn on it. Can I order a new circuit board for it?

By now you mave resolved your prob however.... yes you can order replacement PCB's.
The part # is 27.045
Before you just replace the "blown" pcb you should also check the motor; or, when you install the new pcb you will just blow the new pcb also.( if the motor is faulty.)
To check the motor you will need a multi meter.
There are 3 wires...black, red & blue wires. Using black as the common wire measure black to red..this should be approx 6 ohms, the same when you measure black to blue. Between blue and red you should get about 12 ohms. If you get a short on any of these readings then the motor will have to be replaced BEFORE YOU REPLACE THE PCB.
You don't say what country you are in..these readings and the part number are good for the USA &Canada.
The part # will be different if you have the 240 ss5 E/S model.( has a blue light on the panel.)
Hope this helps.