Active directory not replicating

So this is typically due to a corrupt or dirty shutdown.  Your DFRS event logs should tell you something about this and have you run a command in an elevated command to start the replication again.  What domain functional level are you running at?

If your at 2008R2 take a look at this:
http://blogs.technet.com/b/thbouche/archive/2013/08/28/dfsr-sysvol-authoritative-non-authoritative-restore-powershell-functions.aspx

Also look in your DFSR event logs as well.  They should give you a clue or post them here.

I believe functional level is 2003, although all our servers are 2008. We are not looking to raise level as it obviously wasn't the cause of this mess. We need to know what exactly do we need to do to remedy this. DFSR logs don't have any entries past the power failure; messages before the failure are strictly information, - no warnings et.al. It was recommended that we move FSMO role to another functioning DC, demote problem DC and then promote it back to DC. Is this something that can be done?

Call MS, before you try any other step. Error indicates AD corruption issue. Rebuilding could be the last option. Check this:
http://eniackb.blogspot.in/2009/06/active-directory-database.html

It was suggested to move FSMO role to another DC, then demote and re-promote this server. Will this work? While demoting/promoting the server, will users have access to files that are stored on the server in a separate partition? (except reboot time, of course)

Yes, we do have a backup. What I meant is this. If I demote server, then it becomes just a standalone server. Will shares on it remain share/ntfs permissions and allow users to access the files during the process, except when I am rebooting the server?

Such changes should be done during non-production hours. So, there are no user impact.