Likely the battery on your Sansa is kaput. There are quite a few electronic devices on the market that won't work without an operational battery even when plugged into another power source; your MP3 player may be one of those.
This was bought in August 2008. After connecting my player to my computer to recharge it, the player lights up and says "connected". I don't remember if in the past it said "charging" opposed to "connected". When I turn on the switch, it still doesn't work.
Any advice is greatly appreciated.