Although most Sony video cameras now use inserted flash memory cards or internal hard drives to stored recorded audio/video content, some of the cameras still use an inserted tape (such as a miniDV or Digital 8 tape). If the tape deck door will not close, you need to troubleshoot the hardware. If the tape door stays open you can't record onto the inserted tape.
Remove the tape that's in the Sony Handycam. If the door can close after the tape is out, there is a problem with the tape and you need to replace it. But if the tape door still won't close, the problem lies with the camera.
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Look around the bottom of the tape door and where the gears on the camera draw the deck in. There could be dust or other debris stuck there, preventing the door from closing. Remove this debris and close the door.
Spray a few shots of compressed air into the opening on the tape deck, even if you didn't see any debris. This removes any foreign material from the Handycam.
Turn off the video camera and remove the battery. This forces the Sony Handycam to shut down, closing the tape door.