Vineir :
Ultimately what I did is use a laptop to download the new program that the TPLINK powerline company provides. The UI is WAY worse than the last one as it is only reporting which devices are linked in the network. In my case I used 2 different laptops to track what is being detected on both ends of the connection and each end detected only its own device. Obviously there was no connection between them. In the new UI there is no option to search for devices and the "add new device" feature it mediocre at best. So what I did is reset one of the two devices to factory defaults (this is an option in the new program). After that the connection came back on. Not sure if this was needed or not but then I proceeded to reset the other one to factory defaults as well. After that I had no issues til the time I went to bed. This morning I woke up, turned on the PC and the yellow triangle was there again only briefly though. The connection became stable in 2-3 seconds and was working normally. That being said I don't think that the problem is "fixed" as when everything was ok the yellow triangle (I mean the icon that appears on the internet connection status) doesn't appear at all.
Yet another proof is the fact that before, when the computer was turned off 2 of the 3 lights on the powerline adapter were on (all but the internet one) and all 3 were turned on after the computer was turned on. This morning I noticed that when I turn off the computer now, all lights on the adapter are off. Then the 2 turn on when the PC is starting and after a while the third one turns on as well, and that's when I have internet. Not sure if it's a power-saving thing that got auto-activated somehow or there is another issue but I think this needs further investigation. I'm trying to avoid it but I think I may have to get another powerline link soon.
Lets think about this here, I mentioned it could be the problem I described in several posts, and linked to a site explaining it more. I suggested that you unplug the tp link and plug it back in next time it does it to see if it fixes it. I explained how the ping thing works and why it does work. I even put step by step directions on how to setup a task that automatically does it for you. But, now you have pretty much seen the issue and when you add in the description I'm about to give then maybe next time try unplugging the tp link and plugging it back in and if that fixes it maybe add that task so that automatic pings will go out whenever you are logged in so that the connection stays open.
You say that the 3rd light is off when pc is off and its the Internet light. Ok, well it probably is because there hasnt been activity on the connection and it disconnects when theres no activity. You said the yellow triangle was there for 2-3 seconds after first turning the pc on and then went to normal. Well, apparently some activity went on the line and activated the connection. You may have did a whole lot of extra, but doesn't hurt, just extra. Anyways, if you are hesitant on creating a automated task to start when you login, verify it is the issue first by unplugging the tp link from the power outlet, and back in to see if it fixes it next time it is not working while the PC is on. The PC would need to be on but not in use for however long it normally takes for the network to have issues. When it does, unplug tp link from wall, plug back in, if it works I'd highly suggest you check out what other people have said that have this device and what I tried suggesting from near the beginning.
Check here to verify Im not running you into crazy automated tasks....
https://superuser.com/questions/794744/tp-link-powerline-adapters-randomly-disconnect