Remember, also, that certain apps on certain phones can collide, and can cause this symptom.
This "Addons Dectector" app, for example, when running on several different models of Samsung Galaxy-family phones which are running an Android OS version at or higher than 4.x, works perfectly unless you ask it to actively intercept "push" ads in real time. In order to do that, it must turn-on the phone's "Accessibility" feature...
...not the "TalkBack" feature
within Accessibility, mind you, but just Accessibility, itself; the "TalkBack" feature can remain turned-off for this app.
That's all the app does that's mildly unusual; and it only needs to do it if you opt to have it constantly monitor your phone and block "push" ads... which is a very, very cool feature. In fact, this app is just so cool, it's not even funny. Every phone owner should have it, in addition to a good anti-virus app. And remember that the feature of this app which intercepts "push" ads needn't be turned-on for this app to be useful. In fact, intercepting "push" ads, live and in real time, is only a new feature. Everything else it does, it's been doing for a long time, and, trust me, it's enough. This app is amazing!
On most phones, it works just fine. However, sadly, we who have certain models of Samsung Galaxy-family phones may simply not use the feature where the app blocks "push" ads in real time, because there's an oddity in the Samsung version of Android 4.0 Ice Cream Sandwich and higher which causes the entire phone's "TalkBack" to be turned-on, even though it's only "Accessibility" that the app needs. The dev has tried everything, and no matter what he does, "TalkBack" just won't stop talking to the user of certain Android-4.x-and-higher Samsung Galaxy-family phones if the active "push" ads blocking feature of this app is turned on. That feature of that app -- and ONLY that one feature -- is simply incompatible with certain Samsung Galaxy-family phones running Android 4.x and higher. And that's just the long-and-short of it.
I was reminded of it when I got a new Android 4.1 Jelly Bean phone, and ran the app, and turned-on the active "push" ad blocking, as I had done on my previous Android 2.3 Ginger Bread phone; and suddenly the darned thing started talking to me; everything I did, it told me I was doing. I wanted to throw the phone to the floor; and no matter how many times I turned-off "TalkBack" it just came back on on reboot...
...that is, until I started asking myself what apps I've most recently installed, and then I kinda' went through them in my mind, and suddenly I remembered that that app had some kind of problem like this; and so I looked it up, and, sure enough, there it was, clearly documented. So I simply turned-off that feature in the app, and, voila!, the phone stopped talking to me... even after reboot!
I mention it because from my reading around these and other forums, it seems that there are actually quite a few apps out there which run just fine on all phones until you turn-on a certain optional feature...
...and then all of a sudden, on at least certain phones, all hell breaks loose!
So my recommendation is to look in the phone's "Accessibility" area, specifically at the "Services" part of it, and see what apps are authorized to have "Accessibility" turned-on. Of course, "TalkBack," itself is listed there; and there, by the way, is where you'd turn it off, if it's on. Investigating whether there are any known oddities with any apps that need "Accessibility" turned on will probably lead you to the culprit.
In my phone's case, this "Addons Detector" app that I've been talking about in this posting is also listed there, next to "TalkBack," as an app which needs "Accessibility" turned-on. And as long as I had turned-on the feature in "Addons Detector" that needs "Accessibilility," my phone talked to me even if "TalkBack," itself, was turned off; and "TalkBack" would also turn back on after reboot, in any case. But the minute I went into "Addons Detector" and turned-off real time blocking of "push" ads, then suddenly the phone stopped talking to me, even though "Addons Detector" remains listed, right next to "TalkBack," itself, in the "Accessibility" area, as an app needing Accessibility turned on.
Turning-on "TalkBack," now, makes it work as it's supposed to... annoyingly so, I might add. But if I turn it off, then it actually stops talking to me; and won't turn itself back on on reboot.
So, bottom line: See what apps you have which need Accessibility turned-on by looking under "Services" in "Accessibility" in the phone's "Settings". If any apps are listed there (besides "TalkBack," itself, of course) then there's where you begin researching. An app's dev usually knows which phones have troubles with which parts of their apps, so reach out to the dev, first. Refer him/her to this posting, if you need to, so that s/he can understand what you're asking. Only once you've ruled-out a problem like I've herein described should you start investigating other things.
Hope that helps!