iMac Screen Glitch/Broken?

Hello, JasmeenDH.

That is a sure sign of a failing GPU inside the iMac. There is no software fix for that. The best you can do is hope that it resolves itself temporarily on restarting so that you can backup your computer before you replace it.

What year iMac is this?

You can try a safe mode restart, but I don't think you're gonna get around this that easily.

Let the Mac OS do drive directory repair, cache clearing and other misc housekeeping. Often just booting into safe mode and logging in, then immediately rebooting normally will resolve an issue.  You should do this with all your external peripherals disconnected but the keyboard and mouse. Press the Shift key until you see the Apple logo and progress bar when you restart you Mac.

Booting into Safe Mode… 

Use safe mode to isolate issues - Apple Support

Note– starting up in Safe mode could take 10 minutes or more. Be patient.

Does the problem persist while in Safe mode? 

Restart your Macintosh and re-evaluate the issue.

Great advice from D.I. Johnson, just to add...

Have you blown the dust out of the intakes lately?

What temperatures does this App report, especially GPU?

This App can be used to speed up the fans, all my iMacs would be dead without it.

Never ever ever drop fan speeds below the speed that the Mac itself is calling for.

MacFansControl…

https://www.crystalidea.com/macs-fan-control

I'm not surprised that safe mode was ineffective.

The cost to have a shop replace the GPU is difficult to estimate, but would likely cost as much as a fair, used replacement Mac would cost. And the part is no longer available as new, only used. If you know a good shop, you should start there for a diagnostic, but you should also start looking for a replacement.

If cost is an issue, consider a refurbished Mac direct from Apple. The listings change fairly regularly:

Apple Certified Refurbished Mac - Apple Store

No, replacing the GPU will not cause you to lose your data from the startup drive.

I think your best course of action is to replace the computer and retrieve the internal drive from this one so you can recover the data. You may be able to recover the data from this Mac by putting it into target disk mode and connecting it to its replacement.

As you have been advised, your GPU has failed. You can take it to your local independent Apple Authorized Service Provider and get a quote to fix it, if you don't think it's worth fixing then it's time to replace it.