I've never seen a case of this before.
The way iDevices work is that it first downloads the software, disconnects from the Internet, then applies the update.
I would first download the iPhone firmware on a computer with iTunes from
remember where you downloaded it
Then plug your phone into the computer and put your phone into DFU mode.
There will be a message if done properly that you need to restore your iphone.
On a Mac hold Option on the keyboard, and click Restore. Then choose the firmware you downloaded.
On a PC, hold the SHIFT on the keyboard, and click Restore. Then choose the firmware you downloaded.
If this does not fix your issue, you do have a non related hardware problem. This will require different troubleshooting methods.