You could try a parts store to see if they have some pins but you may have to go to the dealer parts department for them.
Those pins should be āpush-pushā pins. When theyāre installed, you push them in to the first indent and they lock (and are flush), then you can take something small (like a pen) and push the middle in a bit more (about 1/8") and itāll allow the pin to be removed. I know itās kinda late for this info, but hopefully you donāt break any more. 
Chase
Iām sorry but what you really need first is a factory service manual somewhere between $150 - $200. The manual will describe troubleshooting procedures for that model, show locations of all components, give step by step instructions on replacement, and so on. If you know very little, a factory manual is the best learning device.
It should have been a simple matter to determine whether or not the blower motor was running at all or just the air door jammed shut. If the blower motor was not working, a simple check with a volt meter at the blower socket would have told you if the relay and everything else was working, therefore the motor is bad. If the motor was working but no air coming out, that would have been a whole 'nother trouble shooting chart including the air doors which are vacume operated, the HVAC controller, etc.
Iāve had factory manual going back to 1968 for just about every car Iāve ever owned and they are the best way to gain a reasonable knowledge of the car and also to get specific information on what screw to take out to access something. Its what the guys at the dealership use. Even if you donāt do the repair yourself, it is a good way to determine whether it is a job you should tackle or not.
After FINALLY removing the dashboard and purchasing a couple more socket, I was able to access the actuator. I then replaced the actuator, resistor and blower motor. I have to tell you, I really have a huge sense of satisfaction completing this. Yes I could have purchased the service manual but the idea was to spend as little as possible. The air works great! Thanks for everyoneās input and support! I think I might have a new hobby. Do you know if there are any classes to take for basic maintenance, online or in person?
Glad it is resolved. Really the best learning device is a factory service manual. It has all of the information and procedures needed. They are available from Helminc.com for GM and other brands. Yes they are pricey but much more detailed than the Chiltons. You can always get the model specific Chiltons for about $25 for basic information which would be better than nothing. Once you get beyond the basics of oil changes, filters, tire pressure, etc. a manual is really helpful.
I have to commend you on doing that job. Removing the dash on a car isnāt an easy thing to do, especially for a beginner. There may be some classes you could take at a local community college perhaps. There certainly are a lot of books out there you can purchase to study from. Purchasing a factory service manual for the car when you can afford one is one of the best investments a person can make if they want to work on the vehicle themselves. You can also sometimes find CD versions of the manual on Ebay for a very reasonable price.
This is interesting. I didnāt bring this up earlier because I thought it was an anomaly. My daughter had the same problem with her 03 Corolla. I see several people here have had the same problem with their Corolla/Matrix/Vibe models.
Being the type of person I am, I tried to take the blower motor apart. I never got it apart because it is riveted together with some very heavy duty rivets. Anyway, there was nothing wrong with the brushes, but there was some contamination on part of the armature. If the blower motor was shut off while the brushes were on this section of the armature, it would not restart. Sometimes hitting a bump in the road would get it started again.
I managed to clean the gunk off the armature by working through the very limited access provided by the motor design. Now Iām wondering if Toyota is having a quality problem with the supplier of those motors.
It wouldnāt be the first time I drilled out the rivets on a blower motor to get it apart, then used pop rivets to put it back together again. Only thing you have to watch is how the brushes are put in and if you can get them back in again.
For classes, go to your local Tech school. Lots of automotive classes and cool classes like welding.