Here's a solution to fix Nokia 1616 keypad failure, this guide may help to trace a particular keys that stop responding or not working. Just make sure that the keypad membrane is absolutely a clean and free of corrosion before doing anything. The keypad membrane has a tiny round metal and these metals are the membrane switches to a particular keys.
Each keys are connected to a particular group or set of rows and columns.
If all the keys in a particular row or column the problem may possibly lies on the application processor IC, The application processor is the one that controls and the keypad circuit.
If only one or two keys does not work, you may consider it that the problem lies on the key connection lines. If this happen you can mend it by applying a tiny jumper wire to the particular group of rows and columns of where that particular key is being connected. In keypads troubleshooting if one or two keys stop responding, you can consider it that the said keys is being cut to its particular groups of key column and rows.
Outer core connected keys
row a = Right, 7, Send, Left
row b = 9, Up, Down, Soft left
row c = 3, 6, Soft right, #
row d = 2, 5, 8, 0
row e = 1, 4, *
Inner core connected keys
column a = Right, 9, 3, 2, 1
column b = 7, Up, 6, 5, 4
column c = Send, Down, Soft right, 8
column d = Left, Soft Left, #, 0, *