Chosen Solution
When I start my laptop it often crashes (black screen) and restarts again automatically. A message about the problem is then displayed and may be sent to Apple.
It sounds like a hardware problem, I’d guess most likely your hard disk is dying, especially if it runs more reliably once it has successfully booted.The cure would be to get your hard disk cloned to a new one.
Do you have a bootable external drive? If you do I would recommend you boot up under it so you can first copy off anything important. Then run Disk Utility to check the drive from the external drive. If that fails to show any problems then you’ll need to restart your system but this time boot up under Safe mode allowing the system to fix its boot files. If this still fails you’ll need to re-install the OS and/or reformat the drive and install everything back from your backup. For reference: Startup key combinations for Mac