How should I go about troubleshooting this issue? I'm suspecting it's the router/modem that's not able to keep up with so many devices connected to it. If so, is there another VDSL modem you'd recommend for my setup?
Anything else I should be looking at? I appreciate any help!
Some general remarks that might help.
*) Most routers have a web-interface for management. Figure out what the ip-address of your default-gateway is. Type that in your browser. You might need the admin-username and password. If you haven't touched that, it should be in the manual or on a webpage somewhere.
*) Via the webpage of your router you can actually see the details of the state of your router. This includes the state of your DSL-interface. You can see if it is up, how long it has been up, whether it is training, how often it is training, etc. (Training is trying to set up a connection between your router and the router/DSLAM of your ISP).
Note, if you had a separate router and modem, you could probably not look at these things.
Try all the pages on your router and see if there is anything interesting. E.g. see if DHCP leases are good. See if there is any traffic going through the box, into the box, out the box.
*) Text-based utilities are best for trouble shooting. If you have a Linux/Unix box, it probably has more tools than Windows has. In Windows, start a dosbox/command.com and try to get familiar with these:
1) netstat -rn
This shows the routing table. See if there is default route (denoted as 0/0 or 0.0.0.0/0 or 0.0.0.0/0.0.0.0). If so, what is the default-gateway ? Can you ping the default-gateway ? If not, do you have an arp entry for it ?
2) arp -a
This shows the arp-cache. For every ip-address on your local network you are talking to, there should be an arp entry. In normal operations, there should be an arp entry for your default-gateway
3) look at DNS. If you can't reach websites on the Internet, is that just when you use names, or also when you use IP-addresses ? On Linux you have tools like host and nslookup to check if DNS is working. Not sure how to do that on Windows.
4) DHCP.
This is the protocol that hands out IP-addresses. When you have problems, do your devices still have valid ip-addresses ? Can they ping each other (all on the local network). On the webpage of your router you should be able to see DHCP-status.
5) ping.
Mostly useful to ping the end-destination (a website on the net), or your local default-gateway. In any case, you should be able to ping that. if you can't ping your default-gateway, the problem is local, and not your internet connection.
6) tracert (or traceroute on linux).
Read the manpage, or something on the Internet. Can be helpful if the problem is further away towards the Internet, not on your local network. If that is the case, this tool can help determine where the problem, but not fix it.
7) Last resort: a packet sniffer. Check out WireShark. Free and powerful. You can see what is going on on your network in detail. Probably your last resort, as it can take quite a while to get familiar with. If you really know nothing about networking and TCP/IP this is probably useless.
*) Try these tools when everything is working. So you know how things look when there is no problem. When a problem does arise, you might be able to see the difference. If you never looked at normal behaviour, it gets very hard to spot the problem.
With these tools I would do something like this:
there is a problem ->
see if you can login to the webpage of the router ->
if not, check the local network. ping the def-gw, look at arp, look at netstat -rn
if you can, check the status of the DSL interface ->
is it connected ? does it have a lot of errors ? is it flapping ? when was the last status change ? are the traffic counters increasing ?
Good luck.