Q: My computer keeps rebooting and the apple icon has horizontal red lines running through it.

Hey mdbcmurphy,

Thanks for the question. If I understand correctly, the computer is rebooting on its own and the display have red lines on it. I would recommend that you read these articles, they may be helpful in troubleshooting your issue.

Apple computers: Troubleshooting issues with video on internal or external displays - Apple Support

OS X: When your computer spontaneously restarts or displays "Your computer restarted because of a problem." - Apple Support

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Have a good one