Create a totally default style and set that as your site style and then see if it works.
To create a default style, create a new style with no parent:
- Styles & Templates > Style Manager > Add New Style
- Parent Style: No Parent Style
- Title: Default vBulletin
- Allow User Selection: Yes
- Save
Set this as the default in AdminCP > Settings > Options > Styles & Languages > Set Default Style. Then go to Maintenance > Clear System Cache. It is important to set this as the site style so that when someone clicks on the password link, the site comes up in this default style and not your custom style.