I have a 93, 4dr, auto civic. I just ran into this problem this morning. My battery light stays on as soon as I turn on my vechile, I recently put in a new battery so I know this is not the problem. Anyway...The light stays on and for some reason my steering wheel is hard as hell to turn as if I dont have power steerign which I do. I check the fluid its full and I check pullys there fine, what is the problem? My alternator? pleas help

 

The only thing that comes to mind that would cause both to act funny is a loose belt. If the belt that runs your alt and P/S is not tight, it may be slipping. You stated that you checked the pulleys so I am guessing that you have already checked the belts as well.
If they are tight, you may want to try replacing them just to play it safe. They're not too expensive.

 

Most auto parts stores will check your charging system for free. I would definately be suspect of the alternator.