Make sure your tablet is charged. If it still won't turn on, the battery may need to be replaced with a new one. You will need to take the tablet apart and buy a new battery. Click here ASUS Transformer TF101 Troubleshooting for a guide on how to replace the battery.
Your buttons may be dirty or defective. To replace them you will need to take the tablet apart using this guide ASUS Transformer TF101 Troubleshooting.