The SIM doesn't store your information, that is the device's memory. Can you access the iPhone if connected to a PC? Are you automatically backing up to iCloud?
I cannot access the phone connected to my laptop either. The battery is completely dead now. In addition, iCloud stopped backing up along with its issues with Windows 10. My IOS is 8. It no longer updates. It's useless other than slow internet, phone, text, etc.
After trying several charging cables I determined it was internal to the phone and I gradually watched my phone died as I tried to get it to charge.
I was thinking the battery can be removed and charged separately and reinserted so I can at least back up to the computer.