New Router Shows Internet Access but Connected Devices Have None

There isn't enough information to identify the cause yet. The modem type, ISP, and exact make and model of both routers matter. Confirm whether the new router supports your connection type and whether the ISP requires login credentials, VLAN tagging, MAC registration, or another authentication setting. Also verify that the cable from the modem is connected to the new router's WAN port.

Check the new router's WAN configuration first. It may need ISP credentials, a specific VLAN ID, or DHCP instead of a static connection. Since the firmware update was performed while the router was connected through the old router, that does not prove the new router can reach the internet directly through the modem.

Try setting a computer's DNS temporarily to a public resolver such as 8.8.8.8 or 1.1.1.1. If that fixes name resolution, the router's DNS settings or DHCP-provided DNS values are wrong. Also make sure the router's DHCP server is enabled and is handing clients a valid IP address, gateway, and DNS server.

Another possibility is an address conflict. If the modem or ISP-provided equipment uses the same LAN range as the new router, such as 192.168.1.x, routing can break. Change the new router's LAN subnet to something different, such as 192.168.50.x, then reconnect the devices. After changing equipment on the modem connection, power off the modem and router, start the modem first, and then start the router so the modem can recognize the new device.