[TheDopp]

Assuming the program was caching or processing all of the malicious packets it could bog down his computer significantly, but even then the program would simply crash, worst case his computer crashes altogether.

I know that you can connect as many connections as you want through a WRT54G and it will still function normally, because the connection limit for windows is much lower than the router can handle. Maybe if the guy had about 12 devices and each one of them were being targeted separately, but once again there is no way to target a device itself except through the software's external port, and as I mentioned above it would simply crash the program or device.

Attacking a router or a modem directly seems really complicated and contrived if all the person wanted to do was mess with the guy.

Well if the RAM in the router is only 8MB (assuming an older router that's been in the house for a while) the limit is probably 512 or 1024, which even with Windows default behavior of 10 (Honestly have no idea if that was ever changed after XPSP3 since I've been mac since then) that's still Windows saying no - the router is just going to pass the connection attempt along until it's table is full. It's not attacking the router directly, just attacking it being dumb.
Though if I'm way off just tell me and I'll shush. That just always seemed the most logical response in my head to people going 'zomg I've been ddos'd!!11'.