Let's make the assumption that you have a Thomson. If so, it is probably the failure of the
internal power supply. However, it could be dish alignment or a failure of your LNB or a fault with one, or both, of the feed cables. To eliminate a signal problem do you have an old digibox you can test your signal with? It is a good idea to test both feeds.
If the signal is good, the next most likely problem is the power supply (assuming your box is a Thomson). Sadly, Thomson used poor quality capacitors in their power supplies and they are all rapidly coming to the age when they are liable to fail premeturely. Self repair is far and away your best option. You could call Sky but as they are in denial that this is a problem you will probably be supplied with another Thomson that has failed elsewhere and has not been repaired properly (they call these boxes "Refurbished" or "Grade A" but they are usually nothing of the sort and they have an appalling failure rate).
I would suggest your next move would be to open up your HD box (opening instructions
here) and take a good look at the power supply. If you have no idea which board to look at, it is the one that has the two pin mains input socket attached to it. Take a good look at the capacitors, the tops of which should be totally flat. Any with domed or bulging tops, or worse, leaking capacitors, have failed and need to be replaced (don't just replace the dead ones, they are all cheap Chinese rubbish and the lot should be replaced). If you have no idea of what failed capacitors look like, follow thie links in
this post.
To replace you power supply,
Satcure and
Digifix are your best source of complete boards (you remove your board, they send you a replacement rebuilt using much better quality capacitors by return. Obviously, this option means no HD for a few days). If you, or a friend, can solder Satcure can sell you a
bag of the afore mentioned high quality bits to do the job yourself. Do not be scared about opening up the HD box. I can assure you self repair is easy, if you can work a screwdriver you can do it. There is a very good guide as to how to repair it yourself
here. If you really are afraid of performing minor surgery on your HD box, Satcure have a list of local repairers on their site
here. Usually you order a
bag of bits and take that and your HD box to one of these repairers and they will do the work for you.
Thousands of us heve been there before you so there is plenty of help available on here if you need it. Feel free to ask again.
Edit: You have a Samsung, so disregard most of what I have typed above. Test your signal, if this is good, call Sky.