After that, even some particles of the alcalin may be found at the bottom. Wash the contacts preferably w/ only isopropyl alcohol to remove the excess vinegar, although I washed with regular water under the sink (to remove the smell in the plastic), then applied some alcohol and dried the excess w/ a cloth. The black thingie is like a sponge, be careful to dry it well.
Let it dry more for about one hour, just in case. After that, assemble it again, insert the batteries and voilà, working flawlessly.
I considered mine lost and had little hope about this method, but turned out fine, since I noticed there was no electronics in the back housing, just the contacts.
Hope this help you and others.
Disclaimer: Do it at your own risk, I am not responsible for any damage in your device. Just give a shout if it worked for you too and spread the word ;)
I have bumped at the same issue. It seems you can't take it apart; I couldn't, at least. So, since I also had badly corroded contacts and the controller wasn't working anyways, I decided to give it a shot. Believe me, I've tested before posting here.
Try this: Disassemble the whole controller as normal. Remove the B button.
Now, you just have the back w/ contacts. Take a cup and pour alcohol vinegar in. Yeah, that one for salads. Sink the controller in the solution. I recommend doing so vertically, to not soak the black thingies. Inevitably, you will soak one of them, but it'll be ok.
You should notice bubbles coming out. That's the oxygen from reaction, means it’s working. Leave it for about 30-45 minutes.