Get some WD40 and spray it on both ends of the throttle cable and it should loosen it up, esp on the lower end. Also, spray some where the cable connects to the carb. It could be gummed up there as well. Try to work it back and forth gently and see if you can work it free. It might not be a bad idea to spray some underneath the right handgrip and lube that area as well.
That is what a repair shop would do. If that doesnt break it free, the cable may be jammed or damaged.
Good luck!