Well honestly the main test is a NON-wireless connection, powerline adapters are notoriously unreliable especially if your here in the U.S. (we use A/C over in Europe they use D/C for inside homes) and causes all sorts of unreliable results.
At this point your stuck in options, because they all rely on access the Internet and installing / updating the OS in some manner. My main first steps would be normally (with the wired connection)
Did you install all Windows Updates? Including OPTIONAL except BING? Check them and repeat till ALL are installed.
Download and run Slim Drivers, install all the latest updates but you don't need to reboot until you do the last update
Download Malwarebytes do a full system scan (AV doesn't pick up alot of malware) - this resolved almost ALL other similiar posts to date as most had Malware the AV didn't pick up.
Remove whatever AV your using and go to www.filehippo.com and download AVIRA, AVG, Comodo or Panda and do a full system scan - this repeatedly has resolved alot of people issue relying on MS Essentials.
Repeat the AV/Malware scans till the system comes up clean.
Since you can't follow those steps at this point your down to two options.
1) Physically move the computer to the same place the router is, just need Keyboard mouse and screen with the PC, Disable the Wireless (you did do that with the powerline right?) then wire in the connection. Does this prove the problem is the PC itself.
2) Wipe HDD with DBAN, and install Windows Clean. With a Clean windows, and my checklist, do you connect correctly now?
There is no 3rd option to just 'make it work' as we dont' know what it is that is changing it, and I asked very specific questions on what software you have installed that may be doing this to your system.