the favorites dont really go with yahoo. they go with the browser that you are using.
you might have switched default browsers. Most people use either the internet explorer or chrome. the ie icon is a blue e the chrome looks like a color wheel with a blue circle in the middle.
if you can find those on your desktop try each of them and see if one of them has your favorites list and it should also have the cookie to tell your bank that you have logged in from this computer before.
Another thing that you can try if it worked recently is to do a system restore to a day when everything was working correctly. instructions below
I am also able to get you my phone number and log in remotely to work on it with you if necessary but there is an additional charge for that. I will put up the offer if you dont want to take it we can continue working like this.
System restore instructions - windows 7 or 8 8.1
hold the windows logo key down and hit R
type rstrui.exe in the run box that comes up and hit enter
select restore to an earlier date.
Under the "suggested restore" which is usually not old enough to help is a link for "OTHER RESTORE POINTS"
click that if the suggested ones are not BEFORE THE PROBLEM STARTED
choose a date that is BEFORE you experienced the problem
hit ok / restore
the computer will start to shut down
a restoring settngs box will appear with a status bar
when it finishes your computer will restart with the same settings it had on the date you restored to. your data will not be affected.
It is not perfect. But it fixes a lot of things.