Try resetting the Network Connection again. (Settings...System..Advanced System Settings...Network Connection Reset....Reset Connection) followed by a router reboot. For now, try and get one of your Streaming Sticks to connect on the 2.4ghz band. (Although you weren't able to change the Wireless Channels, can you tell what channel you are currently using?)
Some things to verify and consider....
1. Your old modem is unplugged and not broadcasting.
2. You only have one DHCP server enabled. (not sure if you are using a combination modem and router or an ISP modem with your own additional router). If both a separate modem and router are being used, they should have distinct gateways (192.168.0.1 and the other 192.168.1.0). Could be new modem just came w/ different gateway IP than previous one.
3. Other wireless devices are working and have internet access.
Post back with your modem model number, router model number(if applicable) and your Roku Streaming Stick models and any additional info regarding your network setup.
If both your Streaming Sticks are linked to same account, maybe factory reset one (press Reset for 30+ seconds) and see if you can now connect. If we can get 2nd one working w/o factory reset then your channels should be restored somewhat easily between the two devices to save you some grief.
Roku Community Streaming Expert
Just another Roku user... I am not a Roku employee.
Insignia RokuTV, Ultra 4660x, Premiere+ 3921, Express 4k+ 3941