2001 Pontiac Grand Am

I've recently noticed when driving with the cruise control. Then tap the brakes to turn the cruise off the headlights dim (for a split second). I've also noticed recently when very cold the car has to crank a little longer to start. Yesterday, the before the car warmed completely the turn signal flashed faster than normal. Kinda like when there's a bulb burned out, but there's not. I know it's related to some underlying problem. I had the battery checked a month ago, but it was good. The reason I had it checked is because I went to start it one morning and the battery was dead. Please help if you can.

Matt Cole