yunbw wrote:
I'm trying to backup but currently the screen is dead and I cant let my phone to gain access to my phone in order to backup through itunes.
I would have recommended doing that while you still had minimal functionality. If you bring it to Apple or an Apple Authorized Service Provider to request repair, all they will offer is a full service replacement since it will most likely show signs of liquid damage. If that's acceptable to you, then it would be up to you to restore your data to a new device based on whatever backup you have.
If you absolutely need to get the data, it might be possible to get someone to (at least temporarily) install a working screen assembly and then make a backup to iTunes. While the screen is removed, whoever is doing the work can determine if there's any additional damage or if the liquid contact indicators have turned red. This would be going outside of Apple's repair ecosystem, so there's the chance that you might be denied a replacement through Apple. It really depends on whether or not the data is more important than getting an official Apple replacement.