Does the green LED on the LCS WiFi module change after the router reports a successful WPS setup? I think mine went from a fast blink to a slow blink.
I'd take your router up to the Club layout and see if you can get that WiFi module to connect to your router. (Assuming it's not the same make model router as the one at home.) Not ideal since not connecting wouldn't confirm your router is the problem as you have no instance of the Club router connecting to an LCS WiFi module. On the other hand, if your router DID connect to the Club LCS WiFi module you'd know your WiFi LCS module has developed a problem.
I get a red LED briefly when I power the Legacy base/LCS WiFi up (all on the same power strip) but I haven't paid enough attention as to whether it blinks or does any sort of consistent behavior. It would be crude for this day and age (then again it's only come out and sports just 802.11b for crying out loud) but would a power on self test and report back be too much to ask for Lionel?
If all else fails I guess it would depend how long you've had that router. If it's been a few years I think I'd replace it first and get one that supports 5Ghz and 802.11n if not also 802.11ac. At least that way if you still have to replace the LCS WiFi module at least the the new router $s weren't totally wasted. I'd recommend the Airport Extreme if you already have an iPhone or iPad. That way you could be swallowed further by the Apple ecosystem. 
(Resistance is futile.)
