What if I cannot turn on my phone and still needto backup and unlock before getting a new one?

You can disable "Find my Phone" by logging into iCloud.com or the Find My iPhone app on another device.

Review the section, titled: If you no longer have your iPhone, iPad, or iPod touch, in the following support article:

• What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support

If you cannot power it on and boot it, you cannot back it up. What happens if you just plug it in, as that should start it up.