Hi Kyle,
Since you are sure the LCD is in good working condition, then the problems lies on the logic board of the iPad 2, such as:
- The iPad 2 is not producing any image.
- An image is produced but there is no back-light. Usually the back-light filter needs replacement. If back-light is the issue, you can see a very "dark/faint" image on the LCD if you look very carefully.
- It could be that the LCD connector on the logic-board is damaged. Examine it using a magnifying glass. Look for broken/corroded pins, anything damaged/missing/part-removed. Look also around the LCD connector.
- If someone worked on this iPad before, it could have had this issue from before it landed at your desk!
- It could be that the drop or whichever damaged the screen also caused damage to the logic board.
- Could be ESD damage from your or previous repairs.
- I am assuming that the iPad is detected by iTunes when connected to a computer, meaning the image/back-light circuits are damaged. IF the iPad is not detected by iTunes, it could be that the logic board is "dead" or unable to charge and communicate with a laptop. In that case, you have a different set of trouble-shooting steps that you can follow to determine if the issue is with the board or the charging dock for example.
If you are certain the logic board is damaged, you'd better refer this iPad to someone with the tools and the ability to trouble-shoot and repair an iPad's logic board.