Hi, more the likely, when the heater fires up and reaches its limit for the fan motor to come on, the motor has failed. The blower motor is just old and has run until it can't funtion anymore. I hate to tell you this after what you just said, but the only way to solve it is to replace it or have it replaced. They get dust and dirt in the windings and bearings and fail, nothing much you can do but keep your filter clean, but they still fail. You will need to call a tech out to change it. It is possable the capacitor has failed, or the fan relay, but I am 99% sure the motor its self has died. I an sorry to give you this news.
Shastalaker7
A/C, & Heating Contractor