OK, you have my attention now. Obviously I'm doing (or not doing) something different from all those people who've had no problem with this. Maybe this is it.
I haven't read anything yet about changing the PC's IP address. To be honest, I'm not entirely clear on what you mean by that? When I assign a new IP to the router, I'm not doing anything with IP of the PC.
If you mean: after I've changed the IP of the router (from 192.168.0.1 to 192.168.2.2), do I then put that new IP in the browser? Then yes. Still nothing.
Part of the mystery is that I don't have to change the subnet to lose the router. I can make changes to the settings, change the router IP to, say, 192.168.0.50, reboot, use that new IP to access it over and over - until I power it off. Then, still connected only to a local PC, using the same 192.168.0.50 IP I just rebooted to 10 times, still (obviously) on the zero subnet - if I put in that IP: nothing. No router at that address. I have to reset and start over with 192.168.0.1.
So, I can change the IP of the router (to a zero subnet address), without changing the IP of the PC, and still get to it until I power cycle. Why would I need to change the IP of the PC if I change to a "2" subnet?