DIAGNOSIS Classic modem-router handshake issue. The Velop is impatient and times out if the modem doesn't hand it an IP address fast enough after a reboot.
FIX Do a full sequential power cycle. 1) Unplug both modem and Velop. 2) Wait 60 seconds. 3) Plug modem in, wait for ALL its status lights to be solid (can take 2-4 minutes). 4) ONLY THEN plug in the main Velop node and start the setup process in the app fresh.
IF THAT DIDN'T WORK Your ISP might require specific MAC address cloning or DHCP settings. Skip the app setup for a moment. Connect a computer directly to the modem to confirm internet works, then connect that computer to the Velop's LAN port. Use a web browser to go to linksyssmartwifi.com to access the classic setup, which has more advanced options than the app.
HEADS UP Never connect the Velop's WAN port to a wall jack or another router's LAN port expecting it to just work. It needs to talk directly to the modem.