hmmm, fan belt, I'm not sure his unit is that old. I haven't seen a fan belt on a residential furnace ever.
I agree with the low pressure of the gas, the regulator maybe.
Another thing that was eluded to is this, the thing that starts your fan in heat mode is a temperature sensor in the furnace. When the gas first ignites, it heats up the heat exchanger and a temp sensor senses that the furnace has warmed up and then turns on the fan. Also, when the gas shuts off, the fan continues to run until the temperature sensor in the furnace gets down to the shutoff point.
How long do your burners shoot out flames before they shut off? If it's more then about 15 seconds, then the furnace temp sensor that tells the fan to come on may have not been working and the burners stayed on until the high limit temp sensor cut them out, the furnace cooled some and the burners came back on but then the high limit cut them out again. I'm guessing maybe the temp sensor that turns the fan on was flakey or if your unit is new enough, the electronic board malfunctioned and the reset cleared it.
The high limit temp sensor is a safety and keep the burners from running too long without the fan blowing, ie, the furnace would get so hot it would burn up the house.