The first and foremost question is whether or not that NetGear Router is supported by your ISP?
I would hope so but you/he should check the ISP's website list before doing anything.
And I believe that more investigating and troubleshooting is necessary to discover what the current problems may be.
At this time it is going to take a great deal of methodical and planned effort to figure things out. Still unsure about the extent of the full network, its' devices, and corresponding configuration settings.
Especially if the problems are configuration related. A "good" router of any make and model will be problematic if the router and other network devices are not correctly setup and configured.
As for resetting the D-Link: same difference. A reset simply returns that router to its' default/factory configuration. Any devices not set to match that configuration will not or no longer be able to join the network and/or obtain internet access. Things may get worse.
Besides "ipconfig /all" run "arp -a" as well via the Command Prompt. Post both results.
(Redact personal name information.)
You need to know (not necessarily to post) each network device, its' name, the IP address it is using, its' mac, and how the device is connected to the network (wired, wireless).
Also google something like "How to set up a home network" to look for tutorials etc.. Limit to the last year or so.
Read through or watch any that you feel comfortable with.
Objective simply to help you and your stepdad gain sense of the "big picture" and all that you must understand and do when managing your own home private network.