Hi @mtnscott
I am assuming that the router setup and any special routing stuff is all taken care of so that your core can reach the host via TCP. If you can check your router logs, that might bring some clues too.
You could have a hardware problem, but there is more long-shot thing to check. Sometimes the TI "deep update" patch clobbers the MAC address of the TI Wifi chip.
Can you print your MAC address to serial on the non-functional core? There is code here that shows how:
http://docs.spark.io/firmware/#wifi-macaddress
A correct address starts with 0x08 0x00 0x28...
See here for a fix: