Default setting is admin/admin instead of admin/password. You modified the login account? If you reset it to facotry default settings, you should be able to login with admin/admin.

Logs got after reboot won't be quite helpful to figure out the issue since reboot will clear the previous log and restore time settings to default.

Did you try different channels like 1, 6 or 11? If you place the laptop right next to the modem, you still cannot detect it? Try to reset your modem to factory defaults and reconfigure it.

Firewall can be used to control user’s access to the Internet on TD-W8980 and it is disabled in default. http://www.tp-link.com/en/article/?faqid=467

Your MR3420 is running in latest firmware? When the 3G signal drops or becomes 2G, the modem cannot be identified?

Lights go off automatically? Maybe the device is defective?