Your description of the behavior of the ipad1 during a login attempt is more precise than mine, it is the exactly as my ipad1 reacts and supposedly as all other iPad1 will behave. This could be solved either by apple with an update of the safari browser for ipad1. I do not think that apple will do that. Also yahoo could undo the change of the login procedure which they recently made and which is incompatible do the ipad1s safari browser. They hardly will do that either if not be urged by lots of ipad1 users.
!!!! SO SEND COMPLAINS TO YAHOO, PHONE THE HOTLINE ETC !!!!!!
Otherwise you have to buy a new iPad or to change the email provider.