My 2010 13" White MacBook Unibody keyboard did the same thing. I tried all software tweaks but did not work for me. I decided to buy a new keyboard.
I installed it but it did the same thing. So I realized that it could not be the keyboard. I checked the logic board very carefully and found out that some someone had spilled hot chocolate on my macbook.
It had gone down the key 6,7,
T, Y, U,
G, H, J, K,
V, B, N, and M and through the touchpad.
A drip was on one of the tiny component next to the Keyboard flex connection. It was the same thing that had gone in the keyboard.
I cleaned with 91% isopropyl alcohol and blow dried with a hair dryer and also with compressed. I lifted the keys that had got soiled by the chocolate. I took out one of the scissors but that is not necessary because I could clean the other scissors thoroughly while still on the assembly. I took cotton swabs and lightly dipped on that alcohol I mentioned and dried them. I washed the keys I had plucked from the keyboard with warm water to get all the stains out. After drying them well I assembled them and turned on the computer. In fact, this is the same keyboard I am typing from.
I think you all can try this. I was absolutely lucky because the chocolate did not ruin anything. The liquid sensors on the touchpad and the keyboard had turned red which means the liquid had come through. Anyway, if you are careful you can do like what I did. Keep the screws well marked so they don't get lost or not to have extra screws once you close your computer.
Now I have a working computer back again and an extra keyboard I can sell back on eBay or amazon. If you need the keyboard let me know. By the way my macbook model number is A1342. It's a 2010 Model.
The cheapest one goes for $150 on eBay.
All of the keys including the functions keys work 100%
Enjoy life and help everyone while you can.