The log says:
Core server name found in HKLM\SOFTWARE\Intel\LANDesk\LDWM: (core server)
Then it goes on to fail in contacting the core. So what is in that location on the affected machines? Is the core server information correct? If so, is name resolution working for those devices to resolve that name. Also, do they have any firewalls running or security programs that may be preventing communications.
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Of course I modified the log file to remove server specific information. (core server) has the correct DNS entry in the logs. If I connect to the workstation in question and run NSLOOKUP on the DNS name of the core server, it resolves correctly and pings successfully.
I'm not seeing any additional security software on these machines that may be blocking communication.