My old Samsung Galaxy S4 (GT I9500) had issues with all the soft keys (menu and back) and home button. To use the phone in the current situation what I can do is enabling the on screen buttons, is it possible ? The answer is yes and here is How to.
The phone need to be a rooted one
You need to have a File explorer which will help you to access the root folder and edit files (You may try ES file explorer, enable root explorer and grant access Super user permission )
Open the file explorer and go to the System folder (Root/System) and open Build.prop and open it (If you are using ES file explorer it will have an editor too). Add the following like at the end of the file
Save, close and reboot your phone, that’s all you need to do, it will show the on screen buttons on Samsung Galaxy S4 (This will work on other Android Phones too it seems).
If you could not find the keys, make sure the line added to the Build.prop is correct.