As said before, this is something you should leave to a professional, but here is my read on it...
There are actually two systems that generate electrical energy from the pilot light. Both are usually located right next to the pilot burner, on opposite sides of it:
# The THERMOCOUPLE is right next to the pilot, and is usually quite skinny. This generates a small current to tell your gas valve that the pilot is on, and ensures that the gas is turned off if it goes out. The fact that your pilot does stay on means that this is working.
# The THERMOPILE is also right next to the pilot, and is usually the larger of the two. This generates a much larger electrical current from the heat of the pilot flame, and is used to open and close the main gas valve. Usually when you have a pilot, but no main burners, it's either the THERMOPILE or the entire gas valve itself that is defective. If the pilot has deposited a lot of soot on the THERMOPILE, it may also be insulated from the heat and not generate enough current. Check it out and clean it with some emery cloth, and see if this helps. A service person can easily check this.
One other thing that many people forget is to also check the actual On-Off switch, as these can go bad. Check it out for continuity, as this may also cause the same symptoms.