This is not a contamination issue. If your beer were contaminated, you would see lots of activity, and the gravity levels would be falling significantly - you're beer would just taste bad.
There are a couple of possible issues here. One is that the yeast you pitched is, really, truly, dead. That's unlikely, though, if you purchased it from a home brew store with high turnover. (Some packets of Nottingham dry yeast have been reported DOA, but they're mostly out of the brewing system by now.)
It's also possible that you killed the yeast, which is more likely. Did they freeze when you left them in your car overnight? Did you try to make a starter and (for some weird reason) throw them in the microwave?
What's more likely, though, is that the yeast are just getting started SLOWLY. Give them another few days before you freak out. If you continue to see no change in gravity (take lots of hydrometer samples) then you can pitch a second vial/packet/smack-pack of yeast.