Sierra OS not booting up

Try booting the Mac into Target Disk Mode. If you're able to get another Mac to connect to as described in the Apple document and copy the files you need to the other Mac or a connected external hard drive.

At what point in the boot process does it freeze up?

Possibly sound like a failed hard drive.

IF you have been backing up the computer your data is safe, if you have not been backing up, I hate to say it but you are about to find out why backup is absolutely necessary. Going forward please use Time machine to backup.