I found the solution. After searching the web for what seemed like an eternity,
I found the following on a Google Groups page:
[Q]1 - How can I make my PC play a flash file on my local hard drive?
Unless you buy Macromedia Flash (the authoring environment) you can't play
them just straight off, you have to open them with a browser which has the
Flash Player plugin installed. To do this, either right-click on the .swf and
select open with... (internet explorer) or open IE and then go to file...
Then I realized that I started having the problem about the time I got my new
laptop. I didn't install Flash MX on my new laptop because I don't really use
it anymore, I use Swish, so I didn't install it because I hate installing
programs I don't use. Anyways, I installed Flash MX on my new laptop and walla,
I can open .swf files on my machine again.
I didn't realize I had to have Flash installed (the program, not the player)
in order to be able to open .swf files on my machine as opposed to viewing them
in a browser. Guess I know now!
I thought I'd post what I found in case anyone else had the same problem and
didn't realize it.