Samsung DLP model HLR5067W has three horizontal green grid-like boxes

Either bad capcitors, or (if you're lucky) the color wheel needs lubed up. Probably bad caps.

First thing is look at the model number of the TV and make sure of the complete model number. For instance there are 2 versions of this model requiring 2 digital board numbers. If your model is just HLR5067W the part number is BP94-1858A if the model is HLR5067WAX the part number is BP94-02084A. I bet yours will be the later of the 2 since that is a high failure version. They are NOT cross compatible. The parts you can purchase from Samsung at http://www.samsungparts.com
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DMD board is bad

I would suspect the lamp first as they can cause intermittent shut down issues.

if it goes black but the light is still working the dlp chip is failing this is like a small lcd screen that the light use for the piture to work looks like this http://www.fixyourdlp.com/2012/04/24/the-affordable-solution-to-white-dot-syndrome-on-your-dlp-tv/ hope this help you.

move the speaker away from the tv

Greetings!

I hate to be the bearer of bad news, but it is not something that has a quick fix. Without inspecting it myself it is impossible to say, but the last three of these that I have seen have been bad digital boards and can be a real bear to change, even when you have experience.

I would get slightly different video symptoms when I would switch between the coaxial input to the component input to the HDMI input. But in all cases my on screen display and menu were anomally free. Hope this was helpful, even though I don't think it is something you should attack yourself.

Good luck!
Rob

The main board is more than likely the cause of the trouble. Time for a new TV.

what i would do is crack into the tv and watch the individual parts being careful not to unplug anything while you take the back panel off.....turn it on and see what happens. let me know what happens

And the problems are.....?