For the fact that your able to initiate the initial connection to router and it doesnt go into a failed communication mode until you make the change to the IP, can you make other changes without changing the default IP from 192.168.1.1 and have it function or is any other changes with default IP at 192.168.1.1 causing problems.
Its quite possible that the router is partially damaged to where the initial config is accessible and then further changes written to ROM cause for a corrupted config in which it goes out to lunch.
It should also reply with ping requests to the router at the IP that you set it to. So if set to say 192.168.100.1 you should be able to ping that IP and get a response if your not getting a response then try the default IP of 192.168.1.1 if still no response then the router is probably trash and time for a new one. One last effort might be to reflash the router after hardware reset and see if that will re-zero the corruption on the flash ROM back to healthy state.