My faucet stopped working but my dishwasher still works-do you think it's a water pipe problem or do I need a new faucet?

Might be nothing more than a clogged aerator nozzle on the faucet... unscrew that and clean it first.

Is this your kitchen sink, if so, have the pipes ever frozen before? If you are not getting even a dribble I'd guess the lines froze. Back to you