This is a weird one and I've never seen anything like it while doing networking either professionally or for friends. I was going to change some of the settings of my router the other day and found that I couldn't connect to my router at 192.168.x.x.
After lots of troubleshooting (disconnecting all devices, turning off wi-fi and trying a direct connection, etc) I found the only way I could access my router was if I turned it off, disconnected the ethernet cable from the modem (thereby disconnecting my internet), turning the router back on. At this point I could connect to the router either wired or wirelessly.
As soon as I plugged the ethernet cable back in to the router I lost access to my router. Internet access still works, but I can't get to my router's control panel.
To make things even weirder if I disconnect the ethernet cable I don't regain access to the router until I power cycle it. I'm going to take the router to a different house and try it to narrow it down to the actual time warner modem.
What kind of modem are you using? Purchased? Rented? Is it an all-in-one? Are you paying TWC/Spectrum for home-wifi?
You write that your router is at 192.168.x.x.
Are you actually setting up a 16-bit private network?
If your "modem" is also functioning as a router, you could simply have two separate 8-bit netowrks operating, one on 192.168.0.0/24 and one on, say, 192.168.1.0/24, and since the "modem/router" is handing out IP addresses, your devices are on the modem's network, and not the router's network, which is why you cannot connect to your router until you disconnect the modem and the rotuer and reboot.