Apply a small amount of Isopropyl alcohol solution on a lint-free cloth and wipe it on the computer monitor. According to the Crayola Stain Removal guide, spraying the computer monitor with a slight application of WD-40 will remove the crayon stains.
Wipe the computer monitor with a soft micro-fiber cloth to avoid potentially scratching your screen. Electronic wipes also prevent lint and scratching, and can be found at your local or online electronic retailer and office supply stores.
Use a sponge and a mixture of liquid dishwashing soap and water, if the crayon stains are still not coming off. Apply gentle force to the monitor screen in a circular motion so the sponge does not damage the screen. Wipe the soapy residue off with a dry, microfiber cloth.