Can you back up your iphone whilst its on airplane mode?

Last night I went out and to try and save my battery I put my Iphone on Airplane mode. My iphone screen then completely stopped working, so I can't unlock my phone. Does this mean I won't be able to back up my iphone? Is there anyway I can get the phone fixed without having to replace the whole thing?

Its not a matter of it being an AM, its that you can't apparently get any power to it now. Since that is the case then you can't back it up.

You could try taking it to an Apple Store to see what they could do.