I have downloaded Peach.blend but I saw what exactly the problem is at the first view, the bones are not where they have to be or still missing.
I think ninetalescommander and Ploag are right, the way they were exported totally breaks the rig. Example: the bones of the left fingers are on the lips and the mouth and else where, the left wrist is on the idex right finger including the Jaw offset, some of bones the right fingers bones are on the left is the wrong vertex group assigned (they move the fingers of where they are, if it's english)... the names and their vextex groups are different from what and where they should be. And in blender, bones use vertex groups which have the same name of the bones. Some of bones replace others, doesn't works, or breaks the rig.
I'm sorry but to fix this, I think except if you can repair ALL of it: delete the armature and make a new one; or re-export them like ninetalescommander says.
Here is a video I found on model ressources, the first part is maybe not interrested for you but the others may help a lot. Sorry, it's all I can do without doing mistakes. I'll see if I can do more, but right now, for me it would be like hitting my head to pass the wall (only me, maybe not you guys). I hope I've been understandable.
https://www.youtube.com/watch?v=lisp713k38s from VirtualTurtle
I think ninetalescommander and Ploag are right, the way they were exported totally breaks the rig. Example: the bones of the left fingers are on the lips and the mouth and else where, the left wrist is on the idex right finger including the Jaw offset, some of bones the right fingers bones are on the left is the wrong vertex group assigned (they move the fingers of where they are, if it's english)... the names and their vextex groups are different from what and where they should be. And in blender, bones use vertex groups which have the same name of the bones. Some of bones replace others, doesn't works, or breaks the rig.
I'm sorry but to fix this, I think except if you can repair ALL of it: delete the armature and make a new one; or re-export them like ninetalescommander says.
Here is a video I found on model ressources, the first part is maybe not interrested for you but the others may help a lot. Sorry, it's all I can do without doing mistakes. I'll see if I can do more, but right now, for me it would be like hitting my head to pass the wall (only me, maybe not you guys). I hope I've been understandable.
https://www.youtube.com/watch?v=lisp713k38s from VirtualTurtle