I'd like to know if there is currently any way to automatically know
if a visitor to a web page is using dial-up or broadband and then
automatically have them re-directed to the appropriate low-band or
high-band web page without them knowing they are being diverted.

Also, the same question would apply as to whether users have
Macromedia Flash installed on there system.

Short answer: Not possible
Long answer: You could 'generate' some traffic between the client and
the server and check the transfer rate but even then it wouldn't be
viable. There are lots of things that may affect a user's tranfer rate
at a given time.
That's why almost every site offering video clips has 2 or 3 versions
of it, for low, medium or high speed users.

As I see it, you have these choices:
1. Let the user choose
2. Automatically redirect to the low-bandwidth page and provide a link to the other
3. Use user profiles and preferences

Checking for low-high bandwidth, I have no Idea ...

But you can check if a browser has the flash player and redirect to
the suitable page automatically ...

http://www.macromedia.com/support/flash/ts/documents/uber_detection.htm

Good news ... found some code to check bandwidth speed ...

Check out these links ...

Using Flash :
(Both link contain the Same Article)

http://www.sonify.org/home/feature/remixology/019_bandwidthdetection/
http://www.wildform.com/tutorials/bandwidth/

Javascript :

Couldn't find the exact article ... to lazy to go through it :)
Anyway, find below a link to a page that has Javascript coding to
detect bandwidth ... go through its source ...

http://www.emediacommunications.biz/sm8/sm8_example.jsp

Hope that helps. :)

There is no documented way to determine the throughput of a client
from any web technology but there are sevral ways you can check by
creating a custom solution through code.  Flash would be the best way
to do this as you can check the bytes loaded of a streaming media
element in increments and with a little math you can approximate their
average data rate.  Obviously, this would cause a delay on your main
page but it is fairly consistent.

Detecting flash player is very easy also.  I would be willing to help
you with both aspects of this if you're still interested but as of
right now im running late to work.

Let me know!

flashGuRu-