If I'm understanding this correctly, your issue is with Yahoo home page and not with Mail? For one, if your Yahoo home page was working properly, then suddenly stopped one day, it's likely due to a corrupt Firefox profile file. You don't need to uninstall and reinstall Firefox, which would do nothing if you also didn't delete old files. It would just reinstall with the existing corrupt profile.
I'm assuming you tried re-setting your Yahoo home page? Can be done easily by click and dragging the Yahoo favicon or URL over Firefox home page icon, and clicking Yes in the Set Homepage popup?
If that doesn't work, then you need to either create or replace Firefox profile files with an existing working one. First, the quick method. If all your Firefox setups are essentially the same, then you can just borrow one from your other computer.
Backup your existing Firefox bookmarks. Then download
MozBackup and use to copy or backup an existing Firefox install on one of your other working computers. Copy the file to a USB drive or CD, and use that to restore the profile on the computer with a corrupt profile using MozBackup once again. Restore the bookmarks if they are unique.
The other method is to create a new profile replacing the corrupt one. However, you will have to reinstall any Firefox extension addons and settings. First, backup your bookmarks. Then, hold down Windows Key+R, and in RUN, type
Firefox -p and ENTER. Follow the steps to create a new profile, and set that one as your default.
Import your bookmarks and reinstall any extensions. In the future, you many want to use MozBackup to save a copy of each Firefox profile locally, should they ever get corrupted and need to be replaced.