Does the replacement battery come with any charge on it to test?

Most of the time the batteries do come shipped with a charge. If the battery was sitting on the shelf for an extended period of time it may need a charge. If the screen is bad, one way to tell if the device still works is by either letting it charge for a little while, then flip the mute switch back and forth. Most of the time, the settings are left by default and you should feel the phone pulse or it may even make the charging sound. You could also test with a computer. Make sure the computer sound is on and open itunes. The computer should make a sound when you connect the device. If it does but you still have a black screen, you may need to replace the screen.