iPad 2 won't charge and turn on
That's classic symptoms of a working iPad, working charge circuitry and a rechargeable Lithium based battery that can no longer take a charge.

Depending on your budget this might be worth paying for a repair or paying for parts and learning about the process to replace a battery. Keep in mind - lithium cells can be fire hazards and if you modify your iPad - it could present a fire hazard if both the old and new battery aren't handled carefully and all safety features aren't correctly reconnected or present in the replacement parts.