2001 Toyota Solara blower working intermittently

A couple of months ago I had driven my car for about 20 minutes, got out to go into a store for about 10 minutes, got in my car and no air would blow out of the vents. (A/C light was on or if I clicked the A/C button light would go off, outside/recyled air button would go on/off if pushed, etc.) And I could feel cold air 'seeping' through the vents, but not all out blowing. I started driving my car and within a minute it came on and worked just fine (on all fan speeds, etc.)

Since then, this is a constant problem. Sometimes the blower works (and works on all levels) and sometimes it just simply does not work at all. I have tried moving all the knobs, trying different things, nothing will help. Generally within a few minutes, it will come on all of a sudden and then will work fine.

However, the past couple days it wouldn't come on the entire time I was driving (15 minutes or so.) It's getting very hot and it was pouring today and I couldn't get any air to move at all in the car and it was miserable!

I had my car in the shop last week to have a timing belt replaced and had them look into it. (Shop I've used for 30 years.) They said they couldn't 'get it to fail' so couldn't figure out what it was. They mentioned 'relay' but weren't convinced that's what it was.

From what I've read online it could be the blower motor resistor or the blower motor itself. I am not a car person, but I consider myself fairly bright, and the instructions to replace the motor or resistor don't look that horribly difficult.

So my questions are:
a) What do you think is the problem?

b) Can a non-car knowledgeable fix this problem on their own?

Thanks!