The good news is the green light means the platform is up and running. Just to confirm... If you type "http://192.168.1.26:8081" in the address bar of your browser does anything come up? Can you ping 192.168.1.26 from another device and do you get a response? Is 192.168.1 your only subnet?
Sometimes http://hubitat.local will bring up the hub UI. If it does you may want to navigate to Settings | Hub Details and see what IP address it is showing. Once you find it, I'd suggest doing a DHCP reservation on your router for the hub so that it doesn't move around.
Your router should be seeing the hub. Maybe reboot the router?
I would also try a different ethernet cable if you have not yet. There have been very occasional reports of the cable that came with Hubitat being bad out of the box. It is weird you get an IP but it doesn't show in the router, so this probably isn't it, but wouldn't hurt to give it a shot.
Either that or the router issued an IP address which then changed for some reason. I have all mine tagged with aliases and I can't remember what it looks like out of the box. It might be easy to miss the HE entry in the router's DHCP table.
Items I would check in this case - is your DHCP server ONLY enabled on your router? do you have any other devices in your network that can serve or are serving DHCP? Check subnet masks on all involved items - is the mask 255.255.255.0 or FFFFFF00 or /24 on your workstation and your router? Often I see misconfigured DHCP servers. If it's generic (and it looks to be) tell us more about the cable plant as well - is the HE hub plug directly into the router? are there any things like smart switches, vlans, wifi point to points in between the hub and router we need to be aware of?