It sounds like you deleted an object.  Are you familiar with DHCP backup and restore?  You should have the benefit of automated backups.  This article from TechNet describes it in a pretty succinct way for 2008, anyone know if this works for 2012?

https://technet.microsoft.com/en-us/magazine/ff621490.aspx

Maybe you were using powershell to clean up your scopes, but if not, here is a description of using powershell and shows a "whatif" switch that should allow you to see what will happen before you actually delete a scope.  Hope this helps.

https://technet.microsoft.com/en-us/library/jj590677.aspx

Hi again.

Have to go, but wanted to share this excerpt below from Microsoft Server 2012 Pocket Consultant.  (650 pages in your pocket?  Really?)

Although you can enable and configure logging separately for IPv4 and IPv6, the two protocols use the same log files by default. The default location for DHCP logs is %SystemRoot%\System32\DHCP. In this directory, you’ll find a different log file for each day of the week. The log file for Monday is named DhcpSrvLog-Mon.log, the log file for Tuesday is named DhcpSrvLog-Tue.log, and so on.

Also lots of stuff on DHCP that may be useful for you until someone comes along here.  I haven't yet found out if the backups overwrite or create additional backups, since overwriting would wipe out your good backup with your current failing situation.  Also, the missing object the service needs, may not be in the backup related to DHCP service.

i would try removing everything in dhcp (outside business hours) and creating again
if that doesn't work, i would remove that and the dhcp role; add dhcp role again and create scopes

I've tested the solution and it was proven working.