Bingo! I think we've found your problem. Change the patch cable from splitter to modem for one that is 3 metres or more in length. You can neatly coil this up and tuck it away out of site.
I had exactly the same issue a couple of years ago and this fixed it for me. It seems that broadband traffic interferes with digiTV signals when the two units are too close to each other cabling-wise.
Cheers- AL
