There is a good chance that the housing assembly you bought has been sitting in numerous warehouses for the last several years. There is a good chance that the battery dried out.
If you got a voltmeter, you can check the voltage on the pins. Should be around 3.8 volts dc or so, with the left pin being ground. If you plug in the charger and measure, you should see the voltage going up if it is low.. If it stays the same, the battery won't hold a charge, and a replacement battery is needed...
The first thing I change on any iphone or ipod that won't turn on or charge is the battery