You should still be able to backup to a computer you last used to back it up to. I once dipped my phone into the ocean, and after drying out its screen was dead, but it connected and backed up to my computer just fine, even though there was a passcode on the phone and no way for me to enter it. So just make sure you are connecting to the same laptop you last backed up to.
If that does not work, there are some third party applications that claim to back up data from a locked iPhone, but I have never tried using them so cannot vouch for that. Google something like "backup locked iphone".