Yes Sky WILL work, it only connects once a day to the Sky servers by phone. If thats happening each day and you've got it miswired, that will block the internet.
Now, go and look at the phone sockets in the house. (and I mean ALL)
Check where all the cables leading into them run. ALL should be plugged into an ADSL filter. Only the filter(s)should be plugged into the sockets, please check
Of course it could be something completely different - I had a case in Cumbria a couple of years ago where the line went down at roughly the same time every day, and it eventually was shown to be due to a horse having a good scratch and rub on a metal guy rope which was tensioning the telegraph pole....the vibrations affected a weak joint in the cable.