It's possible that your battery just needs to be charged. Make sure the charger is securely and firmly plugged into the phone. Next, make sure the outlet end of the charger is securely and firmly plugged into a working outlet. There is a slight possibility that the phone has been plugged into a non-working outlet. Try plugging in a vacuum cleaner or other device to check the outlet. If, after a few hours the phone does not turn on, it is likely that the battery is dead and needs to be replaced with a new one. This link, Nokia E71x Battery Replacement, will show you how to replace your battery.
Bad Battery Connection
The phone's battery might not be either installed correctly, or might not be making sufficient contact. Try taking out the battery, first seeing if it is indeed installed correctly. If it is, take a Q-tip with a little rubbing alcohol on its tip and wipe the contact points on the battery and the phone. Re-install and see if the phone will turn on.
Loose or Faulty Power Button
The power button could not be making correct contact, making it unable to complete the power circuit. Something to try first, though, before replacing the power button; press really hard on it and hold for a few seconds, wiggling to feel the "click" power buttons make, notifying the user it has been pressed. If the "click" is felt, but still the phone does not turn on, try replacing the power button.
Camera Does Not Work
The camera could not be working because the motherboard is broken, either from exposure to moisture or water, or fried from a power surge. Think if your phone has been subject to any of these problems. If it has, it is likely the motherboard will need to be replaced. This link, Nokia E71x Motherboard Replacement, will show you how to replace your motherboard.
The camera could be broken, or the motherboard could be bad. Are other functions working on the phone? If so, just the camera lens might need to be replaced. If other functions are also not working, the motherboard could need to be replaced. This link, Nokia E71x Camera Replacement, will show you how to replace your camera lens.
Flash For Camera Does Not Work
Flash Bulb Broken
If the flash does not work on your phone, it is possible that the bulb is bad. It is also possible that the software might need to be updated. Go on Nokia's website and download the latest updates. After the updates are installed, try taking a picture that will require flash, or try manually turning on the flash. If that does not work, the bulb most likely will need to be replaced. This link, Nokia E71x Camera Flash Replacement, will show you how to replace your flash bulb.
The Keyboard Does Not Work
If some buttons work and others do not--or all the buttons do not work--it is possible that the keyboard is broken.
The speaker is broken. See if you can call someone and hear the phone ring. If so, it is probably not the speaker. If you call someone, and can see the phone working on the screen, but cannot hear anyone, then it is possible that the speaker is broken.