...And...
Sometimes all you need to do is leave the computer and the modem OFF for more than three minutes in order to fully reset the connection.

Noted.
It really was quite a frustrating - and in the end "funny" - situation. We didn't really change anything major in her computer's configuration except for to add a wireless connection for her modem. We weren't even setting up a WiFi network. It was truly a "plug and play" situation. Thankfully, my brother suggested just to shut everything down for a bit, and then boot everything back up to see if that would fix things... And it did! Apparently, her modem was still "remembering" the previous set up, so it would end up "conflicting" with itself.
My brother even mentioned that he's heard of service calls from his office that go on for hours(!) with people on both ends running diagnostic after diagnostic, and trying fix after fix... When all that was needed was to shut everything down for about 10 minutes.