Are you using the DHCP server in the WGT624 or do you have a server running a DHCP server on the wired LAN? Hopefully, you don't have both running in the same IP address block.
DHCP requests are broadcasts and some router have setting to control how broadcasts are handled. However, that's always between the LAN and WAN side, not between two parts of the same LAN (wired and wireless). By my astute guess(tm), broadcasts should always propogate between the LAN and wireless.
One exception is if the WGT624 has some kind of "client isolation" feature enabled. That is designed to prevent each client from communicating with other clients as in a hot spot. If you have a Linux or Windoze server running a DHCP server on the LAN side, this "client isolation" feature will block everything including broadcasts to the other LAN/wireless clients. No clue if the WGT624 has this feature, but it's present and functional on the Linksys WRT54G.
You might wanna do some DHCP testing with a free tool: