Because your wireless guest network is not using authentication -- and I assume it is also not using encryption -- then the most likely culprit is DHCP itself. Put a LAN analyzer like Wireshark between the AP and the DHCP server, and watch to see whether DHCP requests are actually making it onto the LAN. If not, try capturing wireless packets to see whether the affected station is actually generating DHCP requests. If you still see nothing, look at the configuration of the station itself -- for example, is the DHCP Client service not running or is a personal firewall blocking DHCP? Work your way back through the path until you find the culprit.
Dig Deeper on Network Access Control
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