There's no way to distinguish between a broadband or dial-up as a connection type, but you can make an educated guess by connection speed.
Gmail does this and provides a link to a basic HTML version of their service if they detect it.
(source: nirmaltv.com)
My guess is that there is some client side javascript polling done on AJAX requests. If the turnaround time surpasses a threshold, the option to switch to "lite" appears.
The best part about this option is that you allow the user to choose if they want to use the lite version instead of forcing them.