Good Morning D., sounds like my 3 yo gr son came to visit you ;) Hum that is a toughie, i didn't read the other posts to your question. But I would call a carpet cleaning service and just ask them if there is a way to get it out with out professional service. I loved silly putty as a kid, and found it one time in my tennis shoe. It pulled right out though.
I have had play dough in the carpet and candle wax, kool-aid, pepto bismo all over everything. But never silly putty YET.
If you haven't tried different things yet, might spray it with simple green or a carpet cleaner. I just had a Brain
(f**t) Light come on. No idea if it will actually work. Silly putty is oily, try sprinkling some cornmeal or baking soda on it to soak up the oil in it and see if it will peel up after. Do a small part and see if does anything...lol
Other then that D. call a carpet service and just ask. Can't hurt anything now.
Good Luck to you, let us know what worked
K. Nana of 5
PS I might need to know later also, still have the 3 y/o & his baby brother coming into mischief soon. ;)