Iphone 5s with OK 4G and wifi but no internet connection?

[Colorblend]

Hello forum, I come here in search of your knowledge.

I have an Iphone 5s that started acting up maybe 2-3 weeks ago, what happened was webpages would suddenly stop loading and apps would not be able to contact the internet. Facebook, safari, app store, nothing worked. This did not happen after an update, it just started losing connection. At first it was just every once in a while and the problem would persist for minutes up to an hour. After a while data traffic worked 50 % of the time. NOW it seems to be 1 % of the time (I can never browse the web but once in a while facebook updates slip through).

Strangely, the problem is the same regardless of whether I try to use Wifi or cellular.

I have good connection looking at bars and dots. And when I look at my cellular connection MAC address and everything looks just fine. The connections LOOK healthy but I cannot recieve any data, it has been getting worse also, I suspect some hardware thing.

So far I have tried this:

-Turn off/turn on
-Reset phone (power button + circle button)
-Flight mode on/off
-Tried updating network settings
-Resetting router
-Tried 4g, 3g and 2g
-Updated to latest IOS 9.1
-Turned off Wifi Networking in Privacy/Location services/system services
-Screaming at it


The above is a mix of my own attempts and advice I found on the web. Nothing makes a difference. Previously I got one of the 4S models that had the wifi chip hanging loose when leaving the factory, I have poor luck when it comes to my phone purchases, have I once again bought one that is messed up or is there some intricate software trick that needs to be made?


Thankful for any help

EDIT: I bought the phone in May so it is about 6 months old.

 

[Colorblend]

OK, so I finally got to restoring the phone despite it would not let me turn off Find my Iphone (then you need to enter your apple-ID, that has to be checked through the internet, oh yeah, that was the issue to begin with, no internet).

Now both 4G and Wifi works perfectly, when the Iphone is raw, brand new restore.

But I want all my stuff back, messages, apps and so on. When I install the backup the problem will come back of course. Is there some nice little tool I can use to just install the stuff I want, not settings and all that jazz? I think there may be some corrupt code causing the issue and I would like to keep the phone "fresh" and just get my apps and messages back. I have my contacts still.