Not in the shop right now, but if I recall correctly, on under the home button on the board there is "s" shaped copper connector sticking up. When you press the home button, it presses this connector down. Use a plastic pry tool and "gently and slightly" pull up on the connector. In other words you want to shape it from "s" to "S", just slightly taller. What happens is the "S" connector gets pushed down too much towards the logic board and when you press the home button it can't make contact.
In most cases its a loose connection or you need to reset the device. On the other hand I've actually seen screens go white that are defective. To double check, I hang on to a couple of old cracked screens just to connect up to rule out a bad replacement part. Be careful though, pulling up that logic board over and over to re-connect the (thin cable) to the bottom of the board can be trouble - logic boards have a tendency to snag the power/volume flex cable and tear it, which means soldering and a lot of hassle. I smooth down the power cable with a pry tool and stick on a piece of Kapton tape (after a few "costly" mishaps) before pulling up the logic board. Last, don't use your finger to snap down the cable onto the board -- use a pry tool - gently, because too much force can break off the connector on the logic board and your into big mess.
When you boot up hit ESC and see what message is on the screen. Also, simple enough, try a different keyboard. On systems with PS/2 ports check to make sure the mouse/keyboard is hooked to the correct (green/purple) port. Also try unplugging everything except your keyboard -- I've seen some systems where the keyboard just won't work on certain USB ports. A system will actually run without a battery, but, you have to reset the time, settings, etc, each boot.