LED 1 indicates that trickle voltage from the power supply has been detected. This LED will be ON when the computer is turned off and your power supply is working correctly. LED 2 indicates that the main logic board has detected proper power from the power supply when the computer is turned on. This LED will be ON when the computer is turned on and the power supply is working correctly. LED 3 indicates that the computer and the LCD display are communicating. This LED will be ON when the computer is turned on and video signal is being generated. LED 4 lights only if the computer detects an over-temperature condition. This LED will be OFF when the computer is turned on and running at the correct temperature. More at http://support.apple.com/kb/HT2831]
Put it in update mode. Here's how to do it. First,press the power and home button simultaneously. Then after about 7 seconds release the power button. It should say connect to iTunes. Then plug it into your computer and restore it. It will delete everything on the phone and put the most recent version of iOS on it. If that doesn't work try examing the connector and see if it's plugged in.
Here's what you do. Connect it to the computer. Turn it on, and press the Home button while pressing the power button. Then, let go of the home button. It should say Connect to iTunes. Then, open up iTunes and select Restore. It will delete everything, so make sure you have everything updated on your computer. Let it download and install the software. Then try it out.