This video touches on how to get slime out of a carpet. The main point of the video is that you need to break down the slime with heat. As a carpet cleaner in Tampa FL, I like to use a steamer to break down slime that has hardened on the carpet. If you have a household steamer or a wallpaper steamer, they both work really well on hardened slime.
In the video, the host talks about using hot towels or hot water to break it down but it's just not as effective as steam. I can usually breakdown dried slime in a customer's carpet in about 5 minutes. I can't always guarantee complete stain removal, but I can greatly improve the appearance of the carpet by lightening the stain significantly. In most cases, the stain comes out but it depends on how long it has been there in the first place.
If you have a small wet-dry vacuum or a large one, you can use it to extract the slime once it has been softened. You can use towels and your favorite carpet spot cleaner to remove the broken down slime. Look for a spot remover that works on ink. They work really well on brightly colored slime. If you are having problems getting the slime all the way out it might be a good time to call a professional carpet cleaner, like CHem-Dry of Tampa.