I had a similar problem for months.Yes,it is possible that some channels might still work when your setup is faulty.The technician explained this to me when he sorted out my setup. I tried to call Sky two or three times in the evening after work,but they were too busy.So when I took a day off work,I called them about 11ish in the morning as I thought they might not be that busy.I told the customer services advisor very calmly that I've had it with Sky and wanted to cancel my subscription.I did this after I found this link on Google http://www.weeklygripe.co.uk/a342.asp .I was ready to quit Sky anyway,but thought I'd give it a try.Within a week I had a brand new free SkyHD box and dish.I was chuffed as I've had Sky for years and have never taken out an extended warranty after the first 12 months.I know they might deal differently with everyone calling up,but I reckon its worth trying what I did.If your Sky setup is under 12months old, AFAIK they repair/change equipment for free.
HTH