I had a feeling the Sky subscription cards were paired to the set top box? (i.e. you can't take your card round to your mate's and use it in his box). No idea what the pairing procedure involves but it might be an issue with 2nd hand boxes.
I reckon phone sky and tell them you're cancelling because your box is broken and see what they offer to keep you. 
Kevin
I'm intreigued with this Kevin, we used to have issued cards that we could use in any box, that would pick up most channels, but they use a weird system of switching on/off cards via the sat signal. We could report a card as stolen/missing, and it would be de-activated within a day. An option if you have a spare PC with a big HD is a Skystar 2, a sat receiving card for a PC. You don't need to use Microsplat MCE to use it, in fact it is prob better if you use XP. I have 2 freeview Nebula card in my PC, and am currently recording 3 channels plus watching a forth. I have a Skystar card, but haven't got round to putting the dish up! (time, where does it go ?) Kevin's idea sounds good, if you can't blind them with science, baffle them with bullshit!!!
Ken