Thank you for your reply, Mr. Seaford

The PA4015PKIT has the CPL AV500; two adapters, one of which is installed near the modem, the other I have in the room I mentioned. They are wireless.

I don't recall having to enter any information anywhere, I believe all that needed to be done to activate the devices was to press the pairing buttons. Indeed I never installed the software that came with the adapter until much later.

I hope that answers your questions.

Run the utility for the powerline extender, login its web interface and check its wireless settings. Try the correct Wi-Fi name and password on Vita.
http://www.tp-link.com/en/faq-398.html

That seems to get us closer to solving the problem. However, I can't access the web interface either with or without use of the CD.

Connecting the adapter to my computer does allow the TP-Link software to read the device. The login information the guide hands me (admin, admin) doesn't work, though. The device has a password that goes XXXX-XXXX-XXXX-XXXX; the password field forces me to use upper case letters. Any password I enter that deviates from this pattern is "invalid". The password on the device itself (it's also given in the software's main menu) is "incorrect". I've tried different usernames but always it tells me the password is incorrect. The default username that was entered is Appareil1 (Device1).
I don't know if the software's use of the French language makes a difference; but I'm sure I entered the password correctly, and there's no username printed on the device.

Going the other way and creating a static IP address of the 192.168.1.x type didn't work. It kept telling me it was incompatible with my standard gateway. The error message didn't disallow the settings, but advised me against using them.

What am I missing?

Can you provide a screenshot of login page? It should be admin for both.
You may reset the powerline extender and try again.

Here are the screenshots you requested:

This first image shows the main menu; the password you see here changes when I connect the adapter to the PC (second image). I actually tried this one now and it's correct, except I still don't get directed to the web interface mentioned in the guide.









These third and fourth images show how the menu reads after entering the "correct" password.









Would I reset the adapters by unplugging both and going through the installation procedure again?

I didn't realize that you have no powerline extender...
Units in PA4015PKIT have no Wi-Fi function. To access internet, you have to connect it by wire.
Password in screenshots you provided can be used to add the unit in a powerline network.
http://www.tp-link.com/en/faq-848.html

I apologize if I wasn't clear; I'm not tech savvy as you know.

Connecting my computer to adapter A I was able to add adapter C (I have no B), but it didn't show up in the software menu afterwards. Is that all there is to it? What about the web interface? I don't see any improvement in the signal.

I did have to redo the pairing sequence beforehand, to get adapter A to register on the software.

Your utility is an old version and only the remote powerline adapter can be detected by utility.
As Units in [COLOR=#333333]PA4015PKIT have no Wi-Fi function, it cannot help to improve Wi-Fi signal.

Could you please tell me what the unit is supposed to be for then? And what device you would recommend for the job I need it to do? Thank you.