I had the same problem with my '65 when I brought in home from IL last year in late November. I knew what the problem was as I could smell the rats nest. I pulled the vent to the defroster and found nothing blocking it, so I pulled the heater core and felt up towards the fan motort on the outer box. It was full from the fan motor all the way to the core. So I took a long curved screw driver and tried to break it loose gently. AH, HA HA HA HA! with the fan running I got a face full of the rat's nest out of the heater core hole. also an interior full of rat's nest chunks. So after much running up and down with various length screwdrivers, wire coat hangers, etc., I have heta that blows strong.. I also had to fix the spot where the vent attaches to the heater box on the inside. No big deal. I fabbed up a sort of plenum and used a square boot to attach the two. 

If you can hear the motor running but have no strong flow, it will be either a blockage, or possibly the squirrel cage slipping on the motor shaft. If you don't hear the motor working then that would be the suspect. So rule out the motor first. If your heater core installs from the firewall like mine, then pull it, and look for a blockage in the plenum box on the outside, inspect the heater core itself for fin blockage which will also restrict your airflow, and then look at the plenum box on the inside. I only say start with the outside first if you have a two piece box because it is easiest. If you rule out the easier of the the five going from checking motor running, airflow to the heater core, heater core, then inner box, you will work from easiest to hardest and will quite possibly find the culprit before ending up in a very uncomfortable positiion under the dash. If you have all speeds of fan from highest to lowest, then your fan resistor is working. the resistor is bypassed on high for full speed. It only works on the lower speed settings. if you have a two piece box like min and can pull the heater core from the outside and find that there is no flow then you can check for a blockage. Then you will have eliminated the fan cage and the motor and can go on with your life. this will also make a heater core with blocked fins readiliy apparent (blocked fins and block coolant inlet and outlet are two different things. The heater core may flow coolant freely  but still not allow air to pass through. you whould be able to see a light through the fins if you look through it with a flashlight on the other side). So really if the box is similar to mine, you can do all three outside tests in a matter of a few minutes. If it is blocked on the oustide box wear a mask, turn the fan on high, and gently try and free it with a straightened wire coat hanger. Wear the mask so if it is a mouse condo, you don't end up with a face full of feces.

I hope this helps