My MacBook Pro shuts down while turning on

Restart into Internet recovery, whose code is either in ROM or loaded off the Internet (nothing needs to the right on the drive). For Intel Macs, (Command-Option-R at startup).

Launch Disk Utility and repair the drive.

If no improvement after several passes, you will need to re-install MacOS to make progress.

Use macOS Recovery on an Intel-based Mac - Apple Support

Use macOS Recovery on a Mac with Apple silicon - Apple Support

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The initial "chime" sound is generated in software when your Mac passes the Power-On Self Test. If the chime occurs and/or startup continues, your Mac is working. The blank gray screen should light up. Then on to the disk Drive.

Accessing the Boot drive:

The solid Apple is not in the Mac's ROM at Cold start. The Apple logo can only appear when it is fetched in the first "blob" of software loaded from a 'magic' place on the boot drive, or re-run after a Restart. Then a whole lot of stuff is initialized, and the progress Bar moves part way across. After a cold start, seeing the solid Apple appear says your drive is not completely dead.

Mounting the Boot drive:

The next step requires a lot of files by name, so the File System is initialized, and the Boot Drive is Mounted. If the drive directory is damaged, the drive can not be Mounted, so your Mac begins one pass of Disk Utility Repair. This will take an additional about five minutes. During this process, the progress bar may be extended, and will grow by an additional amount not seen on a routine startup.

at the end of that process (which should not take more than about five minutes), it will attempt to Mount the drive again:

-- if the drive Mounts, boot-up continues.

-- if the drive cannot be Mounted, your Mac can do nothing more, so it powers off.

-- if the process stalls, this may indicate you have Bad Blocks on your Rotating Magnetic Boot drive (if so equipped). The re-reading of Bad blocks can take a very long time (on the order of a quarter minute for each Bad Block).