Router sending packet(s) out every 5 seconds / bandwidth is not compromised

Hi folks, I have a dd-wrt mini router (Linksys WRT54GS v7) which I am worried may be compromised. It is sending out a packet every 5 seconds somewhere despite the fact that my WiFi is disabled (everything is hard-wired here) and all machines are either off or unplugged.

The simple topology would be:

Router --> Modem --> DSLam --> net provider [The modem is an old SpeedStream DSL modem.]

I know that it is not an internal network issue (i.e. not inside the LAN) since all computers are unplugged or off when packets are still being sent out.

I called my net provider but the network admin did not want to take the time to diagnose the issue even though I think this would be the quickest way to diagnose what is going on.

So my question is what would be the best way to diagnose this problem? How would I go about diagnosing it myself? I would like to know what type of packets the router is sending out.