Well, that's a conundrum

First and least importantly (to the conundrum that is), my family is getting a puppy tomorrow. Wicked exciting. He's all neutered and ready to come home. He's a rescue, so we aren't certain what kind of dog he is exactly, but the rescue center knows he's half Chihuahua; they just aren't sure what the other half is. He's a bit larger than a typical Chihuahua, so that's the interesting thing.

Now, to the conundrum, which I'm posting here because I couldn't find any information that was useful, and I tend to find that typing things out helps me think things through better anyway:

My boyfriend's internet often has problems. He lives in an apartment, so there's lots of other Wifi signals passing through that are likely interfering with his, and such. Works fine when plugged into the modem and all that, it's just his computer and mobile devices that have an issue (even then, some days they work fine, and others they don't).

But here's the conundrum-ey bit. On our 3DS systems the local wireless doesn't work at all when the internet isn't. As far as I knew, local play didn't require internet since we're sitting literally 2 feet away from each other. We get error code 018-0000, which means it couldn't connect to the internet, but I don't understand how it's relevant when we're literally sitting next to each other? He doesn't even have his apartment set up as an internet connection for his DS, so I don't know why his internet would even affect it.

Especially since we can go out to the park or something, where there's no internet, and it'll work fine. And it isn't our systems because they work fine anywhere besides in his apartment. It's fine at my house, the park, friends' houses, etc. Just not his.
It works if his internet is working fine, but if it turns off from whatever is causing the shut-offs then the systems stop working too. What's weirder is that it works fine if the power is out.
We make sure that there's isn't anything else on in his apartment that could be causing any extra interference too. It's just really, really odd.
My smartphone is still able to access to the internet no problem (it is not connected to his wifi either though), and I've been using my phone there for far longer than this issue has been happening, so I would doubt my phone has anything to do with it either (I've also checked and turned off my phone when we're testing the systems, and still nothing).

The only thing I can think of is that perhaps something about his modem itself is interfering with the DS signals, or there's some sort of outside interference (which I highly doubt would be intentional)?

Just throwing it out there, but I don't suppose anyone happens to know why this could be happening?

I also just thought I would put this out here because I read about people having similar issues but there were never any responses to their forum threads.