Plugging in router makes wall ethernet port inactive?

I used to plug my computer directly into an Ethernet port in my wall. I live in an apartment complex, and each room has it's own ethernet port. Each room has a separate public IP address coming from the wall. I don't have access to the modem(s).
I just bought a Netgear n750. I plugged it into the wall, and then my computer into the router. It ran fine for about 15 minutes and then suddenly my computer had no internet connection. I reset the router, which did nothing. I then plugged my computer directly into the wall (like I used to), and to my surprise I had no connection. About half an hour later I had internet connection again, but every time I tried to plug my router in, it did the exact same thing. The other rooms in the apartment still had connection, so I tried plugging the router into another room. Again, after about 15 minutes that room's ethernet port stopped working.

To sum it up: Ethernet port in the wall works perfectly until I plug a router into it, then it has no connection.

I used to work for an ISP (simple tech support for about a year) and I am at a complete loss as to how my router could be causing this issue.