Firstly you say the line is noisy only when router is plugged in, so your not hearing a typical dis noise you are hearing unfiltered dsl noise? You mention no nte so i assume star wired setup.
You might have a slight HR but your internal setup needs corrected to be suitable for adsl2, the hr could be any where from the filter to exchange and will show on a pqt test via exfo or jdsu test.
Im assuming you have all connected equipment filtered? If so speak to your CP and book a sfi visit.
Jonny