First, you will need to have the User Manual/Guide for your router to know what screens to go to and what settings to change. Most routers are very similiar but the configuration options can vary in both location and scope. Reading the manual beforehand is always a good idea. You can find the necessary settings and review their current values. Do not make any changes until you are comfortable getting to the desired screen(s).
Second, you will need to have administrative access to your router - meaning some login name and password. Hopefully they are not the default values shown in the user manual. If so that could mean someone else can have, or does have, access to your network.
You access the router's screens using a browser. Type in the router's IP address: Commonly either 192.168.1.1 or 10.0.0.1 and provided in the user manual provided no one has changed the router's default IP address.
Find the setting you wish to change: For example if there is a maximum number of allowed connected devices then you would change that from "5" to maybe "8".
Likewise the DHCP IP range may be limited to just 6 IP addresses. Usually a range such as 192.168.1.100 to 192.168.1.106 for example. If you need more addresses (because you have more than 6 devices) you change the upper end to maybe 192.168.1.108.
As for your LAN cards (i.e., ethernet adapters) they should be set to use the IP address provided by the router. Most likely all is okay there unless the devices are not playing well together when it comes to agreeing on communication protocols. That may be another matter.....
See if you can find the user manual for your router. I have attempted to reason it out abit - please look at this manual:
http://www.downloads.netgear.com/files/GDC/WNDR3700V5/WNDR3700v5_UM_03Sept2015.pdf
You will have to check and confirm. Even if not an exact match, the manual may help you understand more about the router you have and how the configuration screens and settings are presented.
Again we are focusing on verifying that there is not some number of devices limitation contributing to the problem either by count or DHCP address range.
Once that is eliminated then wireless interference would become your focus.