How can I restart when it keeps shutting down

Here is what is happening to you:

The initial "chime" sound is generated in software when your Mac passes the Power-On Self Test. If it occurs and/or startup continues, your Mac is working.

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.

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 Boot drive. The re-reading of Bad blocks can take a very long time (on the order of a quarter minute for each Bad Block).

The solution is to boot into recovery and try to repair the drive, repeatedly, until it is fixed or you are hopelessly stuck.

If you have a trusted backup, you have many options.