LANDesk doesn't have any particular intelligence being used in this area so it is most likely a standard networking issue.
Take a look at this document as it mentions the ports that LANDesk uses. http://community.landesk.com/support/docs/DOC-1591
Remember that two-way communication is involved depending on the function you are trying to use. If you can open UNC from client to core, can you open UNC from Core to client?
How do those machines report their IP address? LANDesk attempts to communicate primarily using the IP address in the database, so is this address resolvable from core (or console) to client? If the IP address that the machines believe they have is different to what is actually required to access them, or somehow something is inbetween acting as a proxy or a NAT then you will have issues.
A few things to think of for now. Ultimately, if endpoints cannot be resolved directly by the core, then you will be stuck with only client-side initiated actions such as policy checks. If you wanted functionality like remote control, the networking would need to be different or you would need to consider something like the Cloud Services Appliance.
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Thank you for this Mark, I will post back with an update if/when we find the problem.