iMac 2009 yellow dots covering screen, won't boot...macOS 10.13.6

+1 Your description indicates the GPU has failed. As the computer has no monetary value and has been obsolete for years (meaning parts are difficult to find) it is not worth repairing. Apple will recycle it for you and please plan on getting a new(er) Mac.

Yes, sadly it is obsolete and not worth repairing.

Give it a good Wake and then recycle it responsibly at your local E-Waste recycler or an Apple AASP.

If you are determined to resurrect your Mac do like den.thed mentioned, contact an Approved Apple Service Provider for repair. Is it economically viable course of action ? You can make your decision once you get the estimate. It'll probably be impressive (the estimate, that is).

Technology moves on, it is wise to replace a computer when it no longer suits your needs. I had a 2011 27" iMac up until about 18 months ago. The reason I got rid of it was it was also obsolete meaning that it would not run current versions of Mac OS and I wanted and needed to stay current.

All software developers design their apps for newer versions of the OS, this includes MS Windows, Unix and other OS's. This means the longer you run an old machine the more you are painting yourself into a corner. A classic example is TurboTax which is a hugely popular app for those that like to prepare their income tax returns because it will not run on their old hardware which is limited by its inability to run current OS's.

This is why if you want to stay current it is not a bad idea to replace your hardware every 7-10 years. Your machine is 13 years old, for a computer it is very obsolete.

Best of luck.