Setup in bold above is new. Modem and WiFi router is provided by the ISP.
When I connect my laptop via a LAN cable to Ruckus Switch [and turn laptop's WiFi off] I can access internet; there by leading me to conclude that Rucks Switch is getting internet; but there is not Wi-Fi internet connectivity.
As you mentioned that, you are able to connect to the Internet via ethernet cable by connecting it to the RUCKUS ICX-7150-C12P Switch. And only unable to connect to the Wi-Fi via RUCKUS Wi-Fi.
You can also check plugging the ethernet cable of the Router, which is connected to the port 11 currently, to any 1 in-12 ports as shown in the below picture.
If that doesn’t work, we may need to factory reset the APs. Please follow the below process to factory reset your APs to configure them with a new RUCKUS Wi-Fi SSID.
IMPORTANT NOTE: To perform a factory reset correctly on one of the access points, you must disconnect the rest of your other access points from the "ICX-7150-switch". For example, if you have 3 access points, you should go to the switch and disconnect 2 of the cables to turn off the "2 access points" and only leave 1 connected with which we are going to work the factory reset once you configure the access point and make sure all is good, go ahead and reconnect the other Access Points back.
In your case, as you have 4 APs. Remove three cables and perform a factory reset on ONE connected Access Point once the factory reset is done, please plug the unplugged Access Points cables back to the Switch panel.
Perform factory reset on web browser as explained below.