Damaged shingles can and do leak, but most of the time, the typical point for moisture intrusion is at the FLASHINGS.
Flashing is the term given to construction components or materials that are designed to seal roof penetrations or terminations. Flashings should be found everywhere a roof meets a wall or other roof, or at any penetration – such as chimney or where ventilation stacks. The faultiest flashing is the plumbing vent boot flashings, whose rubber seal wears out in about 5 to 7 years. Following failed vent boot flashings, other roof penetrations such as fireplace flues / chimneys or gas fired appliance exhausts are the second highest source for moisture intrusion.
After roof penetrations, most of the remaining leaks are from deficient wall flashings. This type of flashing usually consists of sheets of metal, covered with a waterproof material, which are bent or formed to accommodate the angle of the intersection of roof to wall. Sometimes, these components develop leaks from improperly placed nails, or rust, or just driven rain, when not effectively sealed.
Roof leaks are very difficult to locate when it is not raining, but most licensed roofing contractors can use a “spray test” to duplicate natural rain, to aid in locating and correcting the deficient areas. Adding a silicon type sealant is not usually a permanent solution to the problem, so I strongly encourage you to enlist the aid of a professional, licensed contractor when tracking down moisture intrusion.