I see james is going to post, let's see if I can beat him to the punch.
Oh, hell, go ahead James...!
Ok, he chimed in. I'd only add that crappy battery cables or an alternator with one or two phases out could cause this - but in any event, you are describing very low voltage OR very noisy power - either can be a bad battery, horribly bad battery cable clamps (badly corroded or loose) or screwed up alternator.
Oh...... one thing, my car's negative battery cable got REALLY corroded at the chassis end - so bad I bought a new cable and put it on, along with a new fender bolt. Total cost: 1/2 hour of my time and around $12.