Battery Light / Engine Losing Power / Riding rough in damp conditions

My car has 143,000.  I have been the only owner.  The battery light started coming on recently, but only when the car warms up, and even then it doesn't always stay on.  The engine rides rough for a spell when this happens.  When it has been raining out, my car has done this several times -- the battery light will come on and all the needles for the oil, gas, and spedometer will shoot up to their max and fall back down.  It sometimes turns off the engine afterwards, but has NOT ever turned off the engine while driving, only while stopped (but still in drive).  The engine light will come on, too, when the needles are freaking out.  The other day the radio and the odometer's power cut out, too, while driving, after the needles started to shoot up (this time, not in sync).  

The alternator and battery have been tested and are fine.  It was suggested that it might be the battery plugs not getting a good connection.  Someone else thought it might be a computer problem.  Any ideas?