Hi Peter. Welcome to justanswer.
When the phone is connected to the charger, press Volume down and Power key for 10-15 seconds, do you get any response from the phone?
Press down and hold the VOLUME UP, POWER and HOME key until you see Recovery Menu.
Peter, are you using Windows computer or Mac Os X?
You opted for remote assistance, that's why I am asking
I will guide you what troubleshooting you have to do on your phone on a real time basis. Did you press and hold the three buttons which I asked you to hold?
Is is charged?
Let it charge for 15 minutes, then when it is connected on the charger, press and hold power and volume down till it boots up.
Peter, did you get the other documentation in your phone's box?
Did you bought an old phone or a new one?
These are the accessories which you get when you buy a new one
Check the attached image.
For how much did you buy this phone?
You got it for free? It costs approx £362 .
If you have the option to return it then do it as I think there is some defect in the battery circuitry of this device