I've just had the same problem, had my phone for a year now, So I backed up all the apps I want to keep and get rid of those that either don't get used and to reset it and go at everything fresh..
After I removed the apps I went after all the google bs services, [ use my tablet to get the apps ] Removed 'em and restarted/reset the phone...
Thats when the problem appeared.. I opened an app and hit the home button as usual.. it vibrates in response, but no action, long pressed it to bring up the recent/app list..nothing.. I also lost the phones native lock screen/security. I came to find through some obscure search results that google apps lock into/hijack the native files and when deleted, delete those files also..
I put on a keypress logger, and when the home button is pressed, no action and no key ID number showed, but it still vibrates. I tried several remapping apps and the same, vibrates but no action... I then installed another app that allows you to actually edit the key number to app function.. and it replied that 2 .pl files necc to edit were not found or existed.
In the interim I'm using "home launcher",; the launcher app that I installed, snazzy as it is with its software home button, just isn't available while an app is open, so with the HL a simple swipe down from the top brings the home button to view..
Currently waitin for a friend to bring their phone [same model] over and attempt to adb the files and try out a fix.