This happens to me occasionally. I'll carelessly put way too much paper into my paper shredder at once and completely jam it!
The best solution that I've found to this is just using WD-40 to saturate the paper. 💦
Once the paper is saturated and the motor in the shredder is able to run again, you can use something that's fairly rigid but still shreddable to push any stuck paper through the blades, such as the thin piece of cardboard I mentioned in the post's title… or even an unwanted CD if you're really desperate! 💿