Designer users frequently come across this problem while testing their forms/flows. The Submit or Continue buttons do not work even when all the required fields in the form are filled in.
This usually happens when you have a hidden field which is required or which has invalid value. Please check if your form has any hidden fields or sections where the required property is set.
Use Firebug tool in Firefox browser to find hidden controls which are invalid or required and are causing the submit button to remain disabled. In HTML tab of Firebug, search for all instances of s-invalid using the search box at top-right corner of Firebug. This will take you to the HTML of all the controls which are in invalid state. You can generally get the name of the control from that HTML.
Note that if a required control is inside a hidden section, then that section will also be invalid and you will see s-invalid in its HTML. You will have to continue searching further to get to the actual control.