iMac late 2013 stuck in boot loop.

Some internal hard drive failures if they are severe enough can prevent the Mac from booting even from external media.

If you want to confirm a drive failure, then you can create & use a bootable Knoppix Linux USB stick. This may boot since it won't try to mount the internal drive and will usually ignore the errors after a while. If Knoppix boots to the desktop, then you can check the health of the internal hard drive by clicking on the "Start" menu in the lower left of the Taskbar and navigating to "System Tools --> GSmartControl". Within the GSmartControl app, you can double-click the internal hard drive icon to get the drive's health information. You can get the complete report by clicking on the button to "View" or "Save" the report. Post the complete report here so I can review it.

Download the Knoppix v. 8.6.1 DVD .iso file with "EN" in the name for "ENglish". If this version is not available, then use one of the v9.x .iso files. Use the downloaded .iso file as a source for Etcher (Mac, Windows, Linux) in order to create a bootable Knoppix Linux USB stick. Option Boot the Knoppix USB stick and select the orange icon labeled "EFI". Give Knoppix lots of time to finish booting since the Mac may appear to be frozen on the Apple boot picker menu.....even on a healthy Mac it takes Knoppix a while to boot since the initial Knoppix boot process is not updating the video on the display (a Mac firmware issue).

If Knoppix boots, then most likely the general hardware is good and the internal hard drive is most likely bad.

If your iMac is stuck in a boot loop and traditional recovery methods like Internet Recovery and USB boot disk are not resolving the issue, there are a few additional steps you can take to troubleshoot the problem:

1. Safe Boot:

- Restart your iMac and hold down the "Shift" key immediately after hearing the startup chime.

- Continue holding the "Shift" key until you see the Apple logo and a progress bar.

- Safe Boot can sometimes fix issues by performing a disk check and loading only essential system extensions.

2. Single-User Mode:

- Restart your iMac and hold down "Command + S" immediately after hearing the startup chime.

- This will boot your Mac into Single-User Mode, where you can run filesystem checks and repairs.

```bash

fsck -fy

```

- Run the above command in Single-User Mode to check and repair the file system.

3. Verbose Mode:

- Restart your iMac and hold down "Command + V" immediately after hearing the startup chime.

- Verbose Mode displays detailed information about the startup process. Look for any error messages that might give clues about the issue.

4. Diagnostic Mode:

- Restart your iMac and hold down "D" immediately after hearing the startup chime.

- This will run Apple Diagnostics to check for hardware issues.

5. Check for External Devices:

- Disconnect all external devices, including USB drives, printers, and peripherals. Sometimes, a malfunctioning external device can cause boot issues.

6. Check Disk Utility:

- Boot into Recovery Mode by holding down "Command + R" during startup.

- Open Disk Utility and run First Aid on your Macintosh HD (or the name of your startup disk).

7. Reinstall macOS:

- In Recovery Mode, you can try reinstalling macOS without erasing your data. This can sometimes fix system file issues.

8. Hardware Check:

- If possible, create a macOS installer on a USB drive and boot from it.

- Open Disk Utility and check the SMART status of your hard drive. A failing drive could cause boot issues.

9. Professional Assistance:

- If none of the above steps resolve the issue, it might be a more complex hardware problem. In this case, seeking professional assistance or contacting Apple Support is advisable.

Remember that opening the iMac and replacing components should be done with caution and expertise. If you are not comfortable with hardware repairs, it's recommended to seek assistance from a qualified technician.

Thanks for giving it a try. During the boot up process, if it gets "stuck" on the loading bar, it would typically indicate a third-party device driver is either missing or corrupted. However, when booting up in Safe Mode, none of those drivers would be loaded. Since is still fails to boot up, in this mode, it could potentially indicate an issue with either the Mac's internal drive or a the logic board ... most likely, the former.

Before going into replacing the drive, one other thing I suggest that you try is to remove any peripherals (except the keyboard & mouse) from your Mac, and then, boot up in Safe Mode. If your Mac did not have any other peripherals than those connected, then you can forego this step.

Actually, if you have another Mac handy, you could create a bootable startup USB or SSD drive. You would use it to see if you can boot up your Mac. If you can, chances are the issue is not its logic board, but definitely pointing to its internal drive as being a culprit.

Ref: Use an external SSD as your startup disk … - Apple Community

Can you boot the Apple Diagnostics?

Can you confirm your macOS boot disk works on another Mac compatible with the OS on it? Is this a macOS USB installer or a full fledged macOS install on this USB boot disk?

Trying to boot a Knoppix Linux USB stick may be useful. I haven't booted Knoppix on a Mac in a long while, so I forget if any of the boot logs are displayed on the screen of a Mac (they are on a standard non-Apple PC, but I don't recall at what point in the boot process Knoppix gets a video signal on a Mac). If Knoppix shows a boot log on screen at some point & it stalls out, it may provide a clue.

I guess you could try a Verbose Boot even with a macOS USB installer, but if the boot process gets over 50% on the progress bar, then Verbose Mode won't be of any use. To use Verbose Mode, hold Command + V immediately after selecting the macOS USB installer to boot. If successful (and the installer supports Verbose Mode), then you should see the boot log entries fly by on screen. If the boot process stalls during this time, then you may have a clue displayed on screen.

What drive did you install when you replaced the drive? May be best to remove it entirely to see if you can boot into Internet Recovery Mode or to a bootable macOS USB installer.

You must go through all of the steps, not just a few of them. Also, please remember your computer is now 11 years old and it's about time the internal HD has failed. If that is what it is, your best option is simply to replace the computer. Optionally you can add an external SSD which will improve performance however your computer will still be obsolete (it's been classified as obsolete for some years now) . If you would like to go with the external SSD option I'd recommend following the instructions in How to setup an external SSD as your startup disk and also to use the following external SSD.

https://eshop.macsales.com/shop/owc-envoy-pro-sx

Please take a look at the following user tip article, that I authored, to see if it can help you troubleshoot your Mac:

• Mac Basic Startup Troubleshooting Steps - Apple Community