|How exactly does Computer B connect, and, what does it connect to?|
If you do not have a SOHO Router, or combination unit as provided by your ISP (Where the device is the modem as well as a router and Access Point) you should get one and connect it to your modem and then connect your clients to it's LAN ports.
If you do have one of the above (router or combination unit) then you'll want to do the following on both PC's when they're running and connected to the internet:
Step 1. Open your command prompt window: Start >> Run >> type cmd and hit Enter
Step 2. Run the ipconfig command as follows: ipconfig /all
Step 3. Once the ipconfig command has run, click on the "command prompt window" icon in the very top left corner of your command prompt window and a menu comes up. From it, select Edits >> Mark
Step 4. Then highlight as you would in a normal text editor by clicking (and holding) where you would like to start your edit and then drag to highlight all the text you wish to copy and release the mouse button. Then you have two choices. You can either hit Enter and the highlighted portion is copied to the clipboard, or you can click on the command prompt window icon again and go to Edit >> Copy
Now you're ready to paste the copied text into your post!
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.