They are connected by a jack, I've placed them in the green hole on the back and the headphone plugin on the front and no SOUND and not recognized on the volume icon. I tried them on another PC and they work fine. I've searched high and low trying to find a solution and I just get the basics, is the power on, plugged into the green plugin etc.I run Windows 10 on both PCs.
Go into Sound Settings and ensure the correct output device is selected from the dropdown. 

Click on Search on the Taskbar and search for Sound Settings if you don't know how to get to Sound Settings.It's not recognized there as I said in my post. It just shows the USB headset I have plugged in.The headset is likely taking priority...what happens with it unplugged ?I have a headset, external speakers and the TV hooked up to my other computer and it shows all of them in the dropdown. I would think the priority would be the one selected to listen to.

OK, just for fun I unplugged the headset and now I don't have anything showing connected. That would be on the speaker icon in the bottom right corner of the monitor and in the sound settings.Did I ruffle some feathers or SOMETHING?Have you tried another speakers on your pc? TRY to reinstall driversI've thought about trying speakers that are connected by a USB connection but don't know if I have some or even if they make them. Remember, these same speakers that are not working on one PC are working on another. That kind of tells me that the PC that they don't work on has a sound card problem or some kind of limitation or other problems. I've checked on drivers but you can't install a driver on something that isn't even being recognized.

I just checked and it lools like they do make USB powered speakers for a PC.Any Yellow !!'s in Device Manager ? ?No yellows, they aren't listed on the device manager.Which MBoard ? ?Foxcom
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After looking up my Mboard/baseboard, I also tried to look up my sound card and found out it isn't listed. It's supposed to be in the device manager under sound, video, and game controllers. I wouldn't think it would be missing if there were 6 plugins on the back and one on the front? While I was down in the basement looking through all of my computer parts, I did run across 3 sound cards that I haven't researched yet. Only one came with an installation CD but that doesn't matter, I'm almost sure none could be used on my PC.

OK, before I get sent through the dog and pony show, here is a link to my PC spects.https://www.cnet.com/products/hp-pavilion-p7-1510-core-i3-3220-3-3-ghz-monitor-none-series/
The differences are, I upgraded it to windows 10 and the monitor I'm using (HP) only has a VGA hookup. I've piggybacked my DVI plugin with a DVI/VGA adapter that goes to a VGA connection on my monitor. My monitor also has internal speakers which I can't seem to get working. This is my wife's computer and to mess it up would be life THREATENING. She just doesn't like having to use the headset when doing a zoom meeting with her different ladies clubs and relatives. I've been trying to correct the problem to no avail.
PS: My monitor is an HP 2009m.
Oh well, this thread must be dead?I finally found it --- what "it"? Some time back I saw this thread when helping a colleague and even though I didn't need it the amount of detail and all the troubleshooting links caught my attention and maybe something there will help you.  Of course, you may have already seen this at Microsoft, but ...

https://answers.microsoft.com/en-us/windows/forum/all/headphone-jack-not-detecting-headphones-usb/3113fd3c-8608-434b-9817-b4baf30e8138Thanks for the response but the links don't quite DEAL with my problem. It did mention however that I might have to get an HDMI adapter for the jack to plug into which was my next thought anyway. My internal monitor speakers won't work either and may be related to the external speaker problem. Thanks for posting.