The Nissan Path

So my wife's 2007 SE 4x4 has had a wining noise for a couple of weeks now, and only seems to appear after being driven or revving the engine hard. The battery is also questionable. sometimes, especially when its cold, it acts like it doesn't want to start at first. I have been assuming that the power steering pump was wining and the battery was getting ready to die. But this morning she says that it was wining loud and then when she started braking, the engine "stuttered" a bit. Now I thing maybe her alternator is going out. we took it a shop last week, and they told us the tensioner pulley was bad, so I replaced and that didn't fix it. We had the battery and alt checked at AutoZone when the starting issue began and they reported all good. I don't want to spent a couple hundred bucks on replacing a power steering pump or and alternator with out being sure its bad. Anyone have any experience with any of these issues before. Any advice, maybe something I haven't thought of? :? Thanks.

replace battery if its' even questionable
check charging system output, if not up to par, repair as necessary (probably new alternator assy)
any other noises still evident, locate with a mechanics' stethoscope

+1 for the mechanics stethoscope. They're like $10 at Pep Boys and totally worth it.