OK. I found a strange way to get your wallet back. Or at least I think so.
First read, get all you need, then do it offline.

Step 1.
Go to http://gobittest.appspot.com/PrivateKey (actually to a local copy, with your internet disconnected)
put KwFAa6AumokBD2dVqQLPou42jHiVsvThY1n25HJ8Ji8REf1wxAQb into the first editbox
you get 00BF9C46A7C40AAF96ED20CFC0AB0F929D9BE1748AF89B37E9EFB4CDB98DA6B0CB in the 4th editbox.
ignore the first two zeros, keep BF9C46A7C40AAF96ED20CFC0AB0F929D9BE1748AF89B37E9EFB4CDB98DA6B0CB

Step 2.
For this step I modified the known tool "Bitcoin Address Utility" and added some functionality for you.
As I said, my knowledge in Bitcoin / cryptography... could be better.
So, I uploaded this here: https://wsi.li/eQho6D43nn1yV2/1452081
If you go to tools->address utility, at bottom is a test area.
If you paste BF9C46A7C40AAF96ED20CFC0AB0F929D9BE1748AF89B37E9EFB4CDB98DA6B0CB there, a new WIF is calculated and put in the next editbox (5KGg1jDTCw9U3wZKk1XohzRztbpwZtWnBrQEN84ChYAqT6Ev2hR)
That WIF works in Electrum and it is for the address 1Kxrx4WXNBF9dSzDqsJHFjdAEHo8ws1smL

(Edit: clearly use this also offline, maybe on a virtual computer or sandbox)


Now, I know that it's a trust issue here with an exe, I don't even know if the link is not hidden by the forum.
If you PM me an e-mail I gladly post the link again (or I'll simply send it by e-mail). I can also give you the source code, it's 99% the old good "Bitcoin Address Utility", it's in c#, just ask.