Windows 7 Cannot Re-Assign Network Type in Network & Sharing Center

I am fully updated, yes (everyone should try that before posting). I tried The Evil Empire FixIt tool for video issues (wasn't aware it took care of networking issues...but maybe it's a different FixIt tool- I'll DL it and see). And thanks for the registry info; that looks like it might work. I did something else to force "Home" or "Work," but, darn it, I forgot to record the details, and now the MS software has decided that there ISN'T anything wrong with the wireless adapter, and the network map shows a LAN-type diagram. Okay, this sounds confusing, so this is the exact architecture: I got Vonage, which required me to put its non-wireless router between my computer and the wireless modem we get our internet and TV from.; an Ethernet RJ5 cable thus gives me a hard-wired network, and my wireless adapter gives me a wireless network via the modem. For the longest time, my wireless card, although "functioning properly," was effectively blind, so I couldn't see the printer or the OTHER computer. And NOW, I can't see the HARD-WIRED network at all, but it's working, because the PHONE still works. Now I have access to everything I need via the wireless network, but I'll be up the creek if the system decides to remember that maybe it would prefer that I NOT have wireless access. Both of my computers have the same OS almost (one's a W7 64-bit home edition and the other's a W7 64-bit ultimate), but since the other one's connected to the modem wirelessly ONLY, I'm pretty darn sure this one's the offending unit.

I'm reasonably familiar with editing the registry, having just manually fixed a vanishing AutoRun problem on eight of nine drives (one I left default, two never vanished, and Windows kept deciding the six others needed to go...despite remembering the specified labels while ignoring the icon paths). Looking at the related networking entries will allow me to understand the situation more clearly.

[EDIT #1]
My registry is not constructed as detailed in above instructions; there are two entries below this key:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Network
1) Location Awareness
2) NwCategoryWizard
...and two items under the latter, (Defalt) REG_SZ = value not set, and (Suppress) REG_DWORD = HEXADECIMAL 1
...it looks like the last value reflects my instructions that no network be public, but I don't know what else to do there.
[EDIT #2]
I can't use the Evil Empire tool because it want's to use System Restore, and because that utility never works right (it keeps turning itself off and losing restore points), I've turned off System Protection and have deployed Acronis True Image to take over its function, which requires backup to a secure partition that Windows 7 does not use. Microsoft does not make allowances for users who are sufficiently tech-savvy to use different applications to back up the operating system; they do not create the option to back up by other means and then proceed, so the installation of the tool fails.