2001 Honda Civic

I am going to guess that your steering wheel vibes and the car not starting are two separate issues. So, you should probably pick one (which is most serious?) And go with that.

Incidentally, just because the radio works does not mean the battery is good - it takes considerably more power to crank the engine than it does to run a radio.

I would start with doing a battery check AND make sure all cables etc are connected well. Check charging system as well.

As for the vibe, it really is difficult to say from here - it could be a bearing, warped rotor, unbalanced tire.