The Freesat from Sky Cards are not locked to any Box (Even though the initial activation required you to quote the details of the Box is was activated in: Thereafter, its a free agent)
But these Cards go to sleep if not used for a while (As you've found): If one or both are White Card (The Blue House ones are extinct!), then put one of them (Doesn't matter if it is an expired Subs Card or a FSFS Card: They do the same job) in a BSkyB box and leave it (Standby is fine) for up to three days.
Unless it has been switched off completely, it should pick up a refresh signal and come back to life.
Not sure about the HD aspect, though. Someone will know.