Turning phone on if lock button is broken?

If an iPhone is off, and you connect it to a power source (either a charger or computer), it will always turn on. Since you have mentioned that this is not happening, I would conclude that there is something more serious wrong, not just that your power button is broken.

It may be the case that your phone has just 'locked-up' - try holding both the home button and power button for at least 30 seconds and see what happens.

If that fails, I would suggest taking it to an Apple Store and see what they say.

You probably need to some repairs to your hardware (iphone) Unfortunately I do not think it is you button (the plastic piece) but what is behind it.

Here are instructions where to get it and how to fix that

http://www.ifixit.com/iPhone-Parts/iPhone-4S-Power-and-Sensor-Cable-/IF115-011

http://www.ifixit.com/Guide/Installing+iPhone+4S+Power+and+Sensor+Cable/7285/1

Is it easy to do - NO !