It sounds like you are having problems with your proximity sensor. This is what tells your phone that you have that you have it next to your head talking. It tells the phone to black the screen to save battery life. When you take the phone away from your head it tells the phone to show the display. Make sure nothing is covering the area to the left of the M in the Motorola logo under the earpiece. That is where the proximity sensor is located. You may even try cleaning that area.
One of the cures for this that I read about is to take the battery out for a minute. Then put it back in. Sometimes this doesn't work the first time. You may want to try it a couple of times if it doesn't work.
I've never owned one of these nor worked on one. My understanding is that the Original Droid has a slide out keyboard. A guru at the Motorola forum says that if the above fails try this:
You can try to start it up in recovery mode.
1. Press the "x" key on the physical keyboard while pressing the power key at the same time.
2. When the triangle with the exclamation point in it shows on the screen then you need to press the volume up key and the camera button at the same time.
3. When the system recovery comes up use the d pad to move the highlighted words to wipe data/factory reset. and then press the gold key on the d pad.