Do you still have the manual (or can you look it up online) to check the troubleshooting section? They are electronic, so they certainly can give out, but you might find some other things to try if you look.
Mine gets finicky if I don't keep the chest strap clean or if I put the watch part too close to another bit of electronics that interferes.
Is yours doing anything? Does it have a built in watch that still works but won't read out your heart rate? Is the display still ok? Any tears or worn patches on the chest strap?