After getting replacement iPhone 5, it's stuck on white screen

Hi all,

I wonder if anyone has experience with this.

I just got a replacement iPhone 5 after my old one got totally destroyed. The sim card somehow still survived and was sent back to me prior to the new iPhone.

After putting in the sim card and loading my last back-up from iCloud the new phone is stuck on the white screen with the black Apple logo (the power-up screen).

(I've tried putting it into what I think is known as DFU mode (screen turns black with the charger cable going into the iTunes logo).

The trouble is the computer I used to use with my iPhone stopped working ages ago, so I can't really get access to my phone via iTunes.)

Any help would be massively appreciated! Been iPhone-less for a week and half already!

Hunter