iphone 5 internet

My iPhone 5 is connected to the internet and says it has full signal,but when I go onto the internet it doesn't work and says I have no internet connection.😐

I decided to turn off the WiFi and turn it back on and it still isn't working.

I have also turn off the mobile data and 3g and WiFi for the time being < is that a good idea?

I also have broken my lock button so therefore can not turn my iPhone back on and off 😠 Someone told me I can turn it off and then plug it into the charger and it will turn back on, but I don't know if it will work and don't want to risk it and turn on my phone and it not turn back on😐.

I did drop it a month or so ago and a chunk at the top right hand corner is missing,it also has some water within the screen, but it has been working fine until now, so I don't know whether it is to do with that or the phone its self?

Is there anything I can do or will I have to go into an apple store?😟