After changing the domain that the server belongs to, you receive:
Event Type: Warning                              Event Source: NETLOGON                              Event Category: None                              Event ID: 5781                              Date: date                              Time: time                              User: N/A                              Computer: SERVER
Description: Dynamic registration or deregistration of one or more DNS records failed because no DNS servers are available.

The problem is due to old entries in the DNS zone of the previous domain, probably due to a deregistration failure.

Search for the Netlogon.dns file in a sub-folder of the %SystemRoot% folder. Look for lines that begin with a semicolon, like ;5175a911-d70b-4d3c-8df1-024ca6cd6a50._msdcs.company.net. 600 IN CNAME server.child-domain.company.net, and remove the stale records. Then stop and resatart the Netlogon service.