ok with the modem, if you removed the cables & used wireless only would that work or is the modem itself radiating the noise ?
I see its not a wireless modem, but I have one & curious if its worthwhile getting usb wireless sticks ?
Its the Ethernet cables that are acting as an 'antenna' radiating that noise. So removing those 'antennae' and using wireless instead would definitely cut down on the noise. The case of the modem shouldn't radiate much if any. If you must use Ethernet cables, some hints to keep the noise down are:
Use shielded Ethernet cables, and ensure at least one end is earthed.
Keep the Ethernet cable as short as possible, and use as few of them as possible.
Set the speed to 10BaseT. The higher the speed, the higher in frequency into the HF spectrum they'll cause interference.
But eliminating the Ethernet cables all together by using wireless would be the biggest benefit. It certainly helped a lot here.
If its a DSL modem, then the DSL telephone line is also going to be a source of noise as well. DSL is effectively pumping hundreds of RF data carriers down the telephone line at LF, MF & lower half of HF. There's not a lot you can do about that.
If its a cable modem with coax feed, there shouldn't be too many problems with those - just make sure all the connections are tight and unsure good double/triple/quad shield coax is used.