My iMac is in a boot loop

Can you get an external drive to install to?

 Start up from macOS Recovery

To start up from macOS Recovery, turn on your Mac and immediately press and hold one of the following combinations on your keyboard. Command-R is generally recommended, especially if you never installed macOS Sierra 10.12.4 or later… How to reinstall macOS - Apple Support

Command (⌘)-R

Install the latest macOS that was installed on your Mac.

Option-⌘-R

Upgrade to the latest macOS compatible with your Mac.

Shift-Option-⌘-R

Install the macOS that came with your Mac, or the closest version still available.

2. Decide whether to erase (format) your disk

If you need to erase your disk before installing macOS, select Disk Utility from the Utilities window, then click Continue. You probably don't need to erase, unless you're selling or giving away your Mac or have an issue that requires you to erase. Learn more about when and how to erase.

3. Install macOS

After starting up from macOS Recovery, follow these steps to install macOS:

1. Choose Reinstall macOS (or Reinstall OS X) from the Utilities window.
2. Click Continue, then follow the onscreen instructions to choose your disk and begin installation.
3. If the installer asks to unlock your disk, enter the password you use to log in to your Mac. If it doesn't see your disk, or it says that it can't install on your computer or volume, you might need to erase your disk. 

1. Please allow installation to complete without putting your Mac to sleep or closing its lid. During installation, your Mac might restart and show a progress bar several times, and the screen might be empty for minutes at a time.

If your Mac restarts to a setup assistant, but you're selling or giving it away, press Command-Q to quit the assistant without completing setup. Then click Shut Down. When the new owner starts up the Mac, they can use their own information to complete setup.

If you never installed macOS Sierra 10.12.4

If macOS Sierra 10.12.4 or later was never installed on your Mac, macOS Recovery works differently:

• Command-R is still the recommended way to start up from macOS Recovery. This combination makes sure that the installation isn't associated with your Apple ID, which is important if you're selling or giving away your Mac.
• Option-Command-R installs the macOS that came with your Mac, or the closest version still available.
• Shift-Option-Command-R isn't available.

How to reinstall macOS - Apple Support 

Of course you may need to make a USB installer...

Create a bootable installer for macOS - Apple Support...

Create a bootable installer for macOS - Apple Support

Welcome!

Is this the 27-inch iMac running OS 10.12 shown in your equipment profile? If not, what "old mac desktop" is it and what OS is it running?

I have tried holding down command and r etc but with no luck. Thanks

That is for Recovery mode that may not be available to older Macs. Have you tried holding SHIFT whie booting? That is a "Safe Mode" boot. Please see:

How to use safe mode on your Mac - Apple Support

If you get a usable desktop with the Safe Boot, let the computer sit in Safe mode for 30-60 minutes to allow plenty of time for the integrity routines that Safe Mode performs

Please do "About this Mac..." from your Apple menu and tell us the SUB-MODEL of that iMac:

⚠️ For security reasons, please DO NOT post a serial number.

Some sub-models have known issues that may not be repairable or not worth the expense. Example: some 2009 iMac 27" models were the subject of an Apple service programs to replace know bad hard drives.

Any 27-inch iMac will run up to macOS 10.13 "High Sierra" at the minimum. We can work on the update if we get the computer to boot.

Anyway, if you give us those detaisl I requested, we stand more of a chance of getting you moving.

Regards,

Allan