Connection constantly failing on reboot of any device

For the better chunk of the past 4 years, every time any device (be it Laptop, Desktop, iPad, or even Smartphone) on my family's network was booted up and attempted to connect to the internet, the internet would crash across the entire network. It could take anywhere from 2-20 minutes for the internet to return.

However, this is not the case if only one device is in use. For instance, if I am using my laptop while my dad is off of his desktop, there will not be any trouble in my receiving a connection on boot up. If my dad is on his desktop and I try to boot up my laptop, though, the internet will crash for a good while, preventing either of us from using it.

As one might imagine, the family has grown very frustrated with this development, even with our elaborate scheduling so as not to overlap internet usage. Any help would be greatly appreciated.