Have you installed anything recently or force shutdown recently because it sounds like you may have entered a bootloop.... Try mortb suggestion and if it doesnt work try accessing Safe Mode and if all fails you will most likely have to reset....
Boot your Verizon Motorola Droid X in Safe Mode. This will allow you to access the device with the original software and settings if something is preventing the device from starting.
1. Power the Droid X off.
2. Press and hold the Menu button on the lower-left side of the screen.
3. Keep holding the Menu button while the device starts until you see the Home screen load. It should say Safe Mode in the bottom-left corner of the screen.
To take the Droid X out of Safe Mode, simply power the device off, then back on.
From here if it boots you can remove any recent installed apps
Power Device Off First.....
1. Hold Home Button and press power
2. Screen will show a Android with a triangle with astrick
3. Let Go of Home Button and Power
4. Press Search Button (Far Left Button)
5. A blue menu will show at top of page, scroll to Format Device
6. Select Yes to verify
7. Allow format to complete (Information at bottom of page will go through a few steps)
8. Once Format is complete Blue Menu will show at top again, select Reboot
Note: Use volume up and down to select opinion and use camera button as Enter,,,