^
Crummy deal man.
Take a look at this first and I hope it helps.
Turnaround time for both the SIN and Care Card are typically very quick. If I recall correctly, my dad got his within a week from the day we sent it to the day he got his replacement. The same goes for his Social Insurance Card. Good luck!
Edit: In regards to the fee for your BC Care Card, you may or may not be charged for it. My dad, brother, and myself requested a new one and although we sent them a cheque to pay the fee for a replacement, they sent our cheque back saying that it was not necessary.