27 inch iMac, fairly old, won't boot beyond startup screen

Please read the following user tip and restate your question/problem in detail: 

     Writing an Effective Apple Support Communities Question - Apple Community

What model and year is your Mac?

What system version are you using?

When did this start? After a system update?

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

If your Mac doesn't turn on - Apple Support

You may also find the following user tip article helpful: Mac Basic Startup Troubleshooting Steps

If it is older than a 2019 than it is considered obsolete meaning it will not run current versions of Mac OS and vintage meaning parts are largely not available. If this is the case it may be telling you it wants to be replaced and recycled.

Apple Recycling Programs

What to do before you sell, give away, or trade in your Mac