You more than likely have something "phoning home" that the bad guys are tracing back to you.
SO, to track that down, do this in exactly this order:
1. Prepare to reconfigure your router for new IP / MAC, but do not reboot it, yet. Make sure the router is NOT registering with some dynamic DNS service, if it is, that's probably part of the problem. Your ISP may be doing that for you, if so, ask them to change your reverse lookup name.
2. Power down every other computing device on the network. I'm assuming you have a wireless router? If so, track down everything that it connected to it, and power those down too. Save your most trusted device (an iPad perhaps?) for monitoring / reconfiging your router. If necessary, borrow a device from someone you trust.
3. Press "go" to reconfig the router, and observe. Your DOS should go away. If it does not, either the reconfig was unsuccessful, your ISP is somehow part of the problem, the router is registering itself somehow, or the router itself is infested.
4. Assuming the DOS abated, one by one, power up the devices you previously disconnected and observe. If the DOS starts after powering up a particular device, that's the culprit. There may be more than one. Do this slowly, to make sure as you power up a device, it's not waiting some period of time before calling home.
It would not be a bad idea to get your ISP on the phone, explain what you think is going on, and ask them to observe your traffic as you go through the above steps. If something "phones home", and you miss it, they should be able to see the traffic on their segment of the wire.
If you are successful at tracking down a culprit system, enlist the help of the anti-malware vendor in isolating the offending bits. Do this BEFORE you re-image the system. They would probably appreciate a sample. Of course, this assumes you are running anti-malware software on your endpoints.....
Hope this helps.