My interpretation of the question is that you used powerline ethernet adapters, but you lost network connection. You plugged ethernet directly from PC to router, and still had no connection, so it seems that the problem is your onboard ethernet card and not the powerline adapters. You are wondering
- whether there is somewhere in Windows that will tell you if the ethernet card is broken
- whether a usb ethernet card will work to get you back on the network
- whether you need a new PC
To answer 1, you can go to the Device Manager and see what devices are attached to your PC and whether they are working ok. If the network card driver is broken, you'll likely see an error mark. If the card itself is broken it probably won't appear as a device at all.
Why would it break? Maybe a power surge came through the powerline and the powerline adapter didn't shield your computer. Maybe the card is still ok, but you moved your PC and the card was bumped and came loose from the motherboard and needs reseating. Maybe the powersupply is breaking and is starting to slowly kill things off.
To answer question 2, yes, a USB ethernet adapter should work. You may be able to plug it back into the powerline adapter if that looks to still work (maybe look into ethernet surge protection though).
Do you need a new PC? Probably in the next year, as 3-4 years is a typical life span (though some might get to 7+ if you don't need to run new software and you look after it). If more things break, you'll know it's time. I'd recommend making sure all your valuable files are backed up on dropbox/google drive/one drive/external disk in case the issue really is power surge related as another surge could kill your disks.