ABS, Engine, battery warning lights intermittently going on and off

For the past few months the ABS, Engine, handbrake, airbag and battery warning lights come on and off when driving. There is no common theme as to when this happens and I can go for a few days without any lights showing and then the error just starts again. When the lights do come on, the volume on the stereo may dip, there is a slight ticking sound and the speedo may stop working but again this does not happen all the time when these lights are on. I have taken it to a garage who thought it may be the spark plugs, but the problem still happened. They then put a new alternator in and I thought this had done the trick but 2 days later I am now still having the same issues with these warning lights. Any ideas?