, the IP Address issue is a headscratcher. I can't think of a reason for the modem to refuse to hand out an IP address.
As for the web site access, can you try the following when you have time, and that is to switch the modem from dual mode IPV4 and IPV6 operation to IPV4 mode only. To do that, log into the modem, navigate to the BASIC .... GATEWAY FUNCTION tab, and change the Router mode from Dual to IPV4 only. Save the setting. It will take a couple of minutes for the modem to switch to IPV4 mode. I usually reboot the modem after that. To do that, navigate to ADMIN .... DEVICE RESET and run a reboot using the Reboot function. That reboot should ensure that the connected devices all have a singular IPV4 address that they are using. One thing to note, if you run an XBox, you might prefer to have IPV6 enabled, however, it would be worth testing the web site access with IPV4 set as the Router Operating Mode.
For the wifi, please have a look at the following:
Check/set the following 2.4 Ghz wifi parameters:
Wireless Mode: 802.11 n
Channel Bandwidth: 20/40 Mhz, although, for test purposes you could set this to 20 Mhz. In a crowded wifi environment, I would set this for 20 Mhz. It would most likely default down to 20 Mhz on its own anyway.
Wireless channel: AUTO or, to an open channel if one existed, or to the channel that offers the least interference from neighboring routers and modems
WPS Enabled: OFF
Security Mode: WPA-Personal
Auth Mode: WPA2-PSK
Encrypt Mode: AES only
Save the setting and ensure that the Encrypt Mode stays on AES only. If it changes on its own to TKIP/AES, change it back to AES only and save the setting again. TKIP is no longer secure and will cause the wifi data rates to cap at 54 Mb/s which is the 802.11g rate.
Check/set the following 5 Ghz wifi parameters:
Wireless Mode: 802.11 a/n/ac mixed
Channel Bandwidth: 80 Mhz, although, for test puposes you could set this to 40 Mhz. I would revert back to 80 Mhz after running a 40 Mhz test.
Wireless channel: 149 to 161
WPS Enabled: OFF
Security Mode: WPA-Personal
Auth Mode: WPA2-PSK
Encrypt Mode: AES only
Once again, save the setting and ensure that the Encrypt Mode stays on AES only. If it changes on its own to TKIP/AES, change it back to AES only and save the setting again.
Reboot the modem if you had to make any changes, ADMIN ..... DEVICE RESET .... Reboot.
Look at your wifi environment using one of the following applications:
http://www.techspot.com/downloads/5936-inssider.html
https://www.acrylicwifi.com/en/wlan-software/wlan-scanner-acrylic-wifi-free/
http://www.nirsoft.net/utils/wifi_information_view.html
Or,
For IOS
https://itunes.apple.com/us/app/network-analyzer-lite-wifi/id562315041?mt=8
For Android
https://play.google.com/store/apps/details?id=com.farproc.wifi.analyzer&hl=en
In the modem itself, if you have a white CODA-4582 modem, there is a wifi Site Survey under ADMIN .... DIAGNOSTICS. Since it uses all three of the 2.4 Ghz antenna and all four of the 5 Ghz antenna, its fairly sensitive compared to a laptop or phone. The user interface isn't great, but, you can copy all of the data in one go and dump it into something like MS Excel, where you can sort it any way you want.
My personal choice is InSSIDer. Thats the last freebie version of inSSIDer and at this point in time is getting a little old. Its fine for 2.4 Ghz application and does work for 802.11n 5 Ghz networks. It does display 802.11ac networks but not as well as it should. This has become a licenced application now for $20 US and works very well for both frequency bands, 2.4 and 5 Ghz.
The other applications are fine for 802.11ac. Acrylic is graphical, WifiInfoView is text only.
What you want to do is determine what channels in the 2.4 Ghz band offer the least number of users, and in the 5 Ghz band, what channels in the 149 to 165 range are occupied and if so, which offers the least competition in terms of occupancy or signal level for any given channel. If you can find a channel or channel range in that group that is not occupied, that will be the best choice.
Ok, have a look at the wifi settings and at the number of users in the 2.4 and 5 Ghz bands and see if you're able to find a better channel to use for your own wifi network.
Please let me know if the change to IPV4 Mode restores access to the web sites.