Toyota Repair: led light illuminated signifying emission problem, toyota company, toyota corolla

Question
I have a 2002 Toyota Corolla, with about 64,000 miles. I live in Rhode Island.  Car was serviced by Toyota dealer service department for oil and filter change cleaning about one month ago, and car checked for any problems-not assessed by computer; no problems found. The car has not had any major parts or repair problems, and has functioned very well. The service cost me about $32.00(to indicate to you it was a minor service). Four days ago LED light came on.
I called the Toyota service agent about the light and he confirmed I may have an emission problem, but that it may be caused by a loose gas cap.  I was told to loosen and then retighten the cap, and wait about 2 days to see if light disappears.  It has not.  I was told that the car would need to be brought in, attached to computer to assess the problem; that I would be charged $98.00 for the assessment before diagnosis, or repair.
I read your information about Toyota Company indicating it provides an extended warranty for emission system repairs of Toyota cars at no cost.  Is that true?  Would it cover my car which is a Corolla model later than 1996 and 1998?  I will bring my car to the Toyota Service office, with your statements and the link indicating Toyota statement about extended warranty, if that turns out by computer to be a problem. What component of the emission system usually causes the light to come on?  Is that known and reported? I have read about what the components of the emission system are and their function.  I appreciate any information you may be able to give me.  Thank you.

Answer
Before I can answer any of your questions I would need to have the diagnostic trouble code (DTC).
There are many reasons for the light to turn on, most major emiision control components such as catalityc converter and the ECM are covered for 8yrs,80,000 miles under federal emission control warranty so it would seem that your corolla is out of warranty due to the time since it was sold new. Extended warranties are usually purchased by the buyer/customer from either toyota's extra care program or another third party provider.