The router seems to work fine but read above the modem has no default gateway also I can access the routers settings through its default gateway and can still access other device if I add them to the network
How do you know the modem has no Gateway, is the router telling you this? If your computer is telling you you have no gateway then it's your routers problem.
Try isolating the modem.
Unplug the modem from the power and from the router
Plug your computer in to the modem through Ethernet
Plug the modem back in
*You need to power cycle the modem when plugging in a new device, so if your modem has a battery you will need to unplug that as well
Check and see if your computer has internet.
If it does then there is an issue with the router, if it doesn't then there is an issue with the modem