Your cleaning service should involve all aspects of your duct work to maximize energy efficiency and air quality. This includes attending to the heat exchanger, blower, drain pan, plenum and coils as well. In the process, your service provider may find that you're facing larger issues than debris and build-up. The professional may recommend having your furnace repaired if they notice, for example, damage to your heat exchanger or blower motor. Generally, a furnace repair costs between $130 and $500. They may also find that an A/C coil needs to be replaced rather than cleaned and would then recommend A/C repair.
You should be aware that although a substance may look like mold, a positive determination of whether it is mold or not can be made only by an expert and may require laboratory analysis for final confirmation. For about $50, some microbiology laboratories can tell you whether a sample sent to them on a clear strip of sticky household tape is mold or simply a substance that resembles it.