Asus Dark Knight RT-N66router connected to internet but I can't browse

I have this router configured to the latest firmware (9.0.0.4.380_2695). The router is connecting to the computer and mobile okay. Computers show the internet is connected. But I cant browse using any of the machines. When using ping on a computer it fails while from within router interface it works. In the browsers I keep getting error such as DBN_PROBE_FINISHED_NXDOMAIN and others of similar sort. When I connect the computer directly to modem, it works flawlessly. Any help please?

The same issue faced in the previous firmware version. The issue is there for the last 15 days. It was working okay before that for many years. Additionally, it heats up to an extent that I cannot touch the reset button.