This sounds like a job for the professionals or a new carpet. If you don't know what the stains are it is hard to treat.

If it's gum you might try freexing with an ice bag--baggie with ice--and scraping, and a spot treater for the rest, but beyond that I'd leave it to the pros

Yeah, but if the alternatives are expensive professional cleaning or even MORE expensive new carpet, then what do you have to lose by attempting to clean them?

I'd always attempt to clean stuff rather than replace it. I can clean almost anything out of almost anything. I'd start with Spot Shot (aerosol) after manually scraping up as much goo as possible.