MacBook will not fully boot into MacOS

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 screen should light up and draw a blank gray screen. 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 was able to produce the software that contains the Apple logo.

If a prohibitory sign appears at this point, it indicates some fundamental part of MacOS is damaged or wrong version.

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 does a controlled shutdown.

-- 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).

so try booting into Recovery and attempt to use Disk Utility to repair the disk. If it comes clean after several attempts, you are free.

if it fails to come clean, there is much more work to be done, and how you proceed depends on whether you have Trusted recent backups.

if it continues to shut down, you will need to "make it right" to make progress.

typical suggestion would be to re-install macOS, but if the drive won't MOUNT, you are stuck. (you can't read or re-write ANYTHING onto a drive that won't Mount.)

IF and only if you had adequate backups and could afford to lose all the copies of the Files on that drive, you could ERASE the drive, re-install macOS, and restore your files from backup.

If you do NOT have adequate backups, you need to boot from an external drive, and attempt to rescue your files by copying off the damaged drive. If you don't have an external drive to boot from, you need to add a drive and install MacOS on it from recovery. if your Mac has T2 protection or Apple-silicon, you can only boot from an external drive AFTER you have adjusted the security settings to allow booting from such external drives.