1996 Pontiac Grand Am what's the problem?

1996 Pontiac Grand Am 6 cyl Automatic

I have a 1996 Pontiac Grand Am. It starts up fine and idles fine. I can be driving along just fine then it gets to where it won't shift. When I come to a stop and accelerate again it won't shift from overdrive to first. I have to shift it manually. And then sometimes it doesn't want to shift from first gear so I have to give it a whole lotta gas and then let off and it will shift. But sometimes it runs like a brand new car. Recently the speedometer starting jumping and only works part time. The gas gauge also jumps. My day time running lights also only work part time. Not sure maybe an electrical problem? A friend told me that it may be the speed sensor located on the tailshaft of the transmission. Any help will be greatly appreciated. Thank you!