From my original comment:
If you placed an existing RAID set into new hardware, then the hardware ID of the server is no longer the same. This means that the computer profile for the server in AD is no longer valid. Ultimately, it is not a user account password that has changed, but a computer account password that is set by the hardware at domain join. You would have to rejoin the server to itself in order to rebuild the AD account.
This is one of those problems that is only made worse by 2012 Essentials.
From what I know, 2012 essentials requires that it is the only domain controller on the domain, which means my usual approach of demote domain controller, remove from domain, readd and then repromote probably won't work here. I mean, you could certainly try that as well, but lets try for something that doesn't have a likelihood of destroying your AD domain.
Use the standard for workstations
This particular command is the standard for workstations when they have lost their domain trust. On a primary (and the only) domain controller, it should still work. This of course, really depends on how Essentials wants to handle it. Still, it is probably the best place to start.
resetpwd /yourDCfullyqualifieddomainname /userd:domain\username /passwordd:password
This command can and will also reset trust relationships on domains running more than one domain controller. As long as there is one domain controller fully functioning, it works. It isn't clear, however, how it will function in your domain. If it doesn't work, try the below.
In this example, we are going to try and skip the steps that might wipe out an existing domain, and simply re promote your server to DC. Ultimately, this should recreate the AD trust relationship which is likely broken. Taken from here the process looks a bit like this
$domainName = "cohovines.com"
$domainAdminCredential = Get-Credential
$dsrmPassword = (ConvertTo-SecureString -AsPlainText -Force -String "YourDSRMPassword!!")
Install-ADDSDomainController -DomainName $domainName -InstallDns -Credential $domainAdminCredential -SafeModeAdministratorPassword $dsrmPassword
The above script assumes you remember your restore mode password. If you do, this should work. If you don't, things likely got a lot harder.
As a complete aside, I really do recommend having two domain controllers. The process of demote, unjoin, rejoin, and promote is significantly easier in this case.