How do you turn on a iphone 4 when your power button doesn't work and your phone wont charge?
If you plug an iPhone into a charger it should power on. If it's on but frozen, you could connect to iTunes and reset/ wipe it, but that might lose some data depending on your backup situation and what is on the phone. 

If it doesn't, then there is a hardware problem and you'll need to get that fixed or live with a faulty device.