My White 13" MacBook (the last model ever produced) will no longer turn on, and the charger light won't even luminesce when plugged in.

My MacBook has been suffering for the last 2 and a half years or so, and finally called it quits today.
There were many things wrong with it, but the most debilitating issue was with the battery; if the computer wasn't plugged into a wall, it would immediately die. Upon being powered back on, the clock would always be reset to 12/31/2000 at 7:00 PM. As I stated in the title, it will no longer even power on or recognize a charger. Help would be much appreciated. If it's a battery issue then I can replace it, but I don't want to buy a new battery if my computer is totaled.