Uninstalled system menu and wiimotes won't sync

I recently installed Priiloader and after watching this, decided test whether uninstalling the system menu would remove Priiloader (since nothing was mentioned in the changelog, I figured that it would, but I decided to try it anyway). So, I uninstalled the system menu. Well, my wii is set to 16:9, but when I returned to the Homebrew Channel after uninstalling the system menu, it displayed in 4:3. Also, my wiimote would not sync. I tried to exit to the system menu, but the Homebrew Channel just reloaded itself. So, I powered off the wii and tried to turn it on again with the wiimote, but it stayed off. Then I turned it on with the button on the wii, verified that Priiloader was indeed gone (it was), and went back to the Homebrew Channel.

Then, I loaded Dop-IOS Mod and installed system menu 3.2. After it finished installing, I returned to the Homebrew Channel and tried to exit to the system menu. However, my wii just displayed a black screen; it did not reload the Homebrew Channel this time. My next thought was to reinstall IOS 30 v1040, so I went back to the Homebrew Channel, loaded Dop-IOS Mod again, and was about to reinstall IOS 30, but Dop-IOS Mod stated that it was already installed, so I didn't bother to reinstall it. All of this time, I had to use a gamecube controller because my wiimote would not sync.

Next, I went into the information section of Bootmii to verify that it recognized that a system menu was installed. As usual, it said that I had system menu 3.2u, the expected NAND FS usage and such. At this point, I decided to just restore a NAND backup, which of course fixed the issue.

Anyway, there are a few things that I wonder about this.

1) This may be a stupid question, but how could uninstalling the system menu unsync the wiimotes?
2) Why did the removal of the system menu change the widescreen setting, but not modify the internet settings (Dop-IOS Mod was able to download system menu 3.2, so it could still connect to the internet)?
3) Does this mean that some issues that seem like bluetooth module failure may actually be software issues?
4) Could this have been fixed without restoring a working NAND backup? And, if so, how could it be done?
5) Why couldn't I access the system menu after installing it with Dop-IOS Mod?

Thanks for reading this, I hope that it made sense. Please discuss, but let's not turn this into a discussion of how bad of an idea it is to uninstall the system menu. I am well aware of that.

1. Wii Remote synchronisation is part of System Menu, when it is removed the settings are deleted (when it is update they are preserved)
2. Display settings are also part of System Menu, but WiFi settings must be stored elsewhere on NAND
3. No. Bluetooth module failure is always fixed by replacing bluetooth module, so it can't be software
4. Probably if you HAD installed IOS30 (old version, non-stub) it would have been fixed.
6. I'm guessing you had a stub IOS30 which was the reason for System Menu not loading when you installed System Menu 3.2, but didn't reinstall IOS30.

Quote
Sif Jar
No. Bluetooth module failure is always fixed by replacing bluetooth module, so it can't be software

Actually, I ment that since my wiimote would not sync or turn on the wii even after reinstalling the system menu, it seemed like bluetooth module failure. In a situation similar to this, where a system menu is installed but does not work and the wiimote does not turn on the wii, it is usually assumed to be a bluetooth module failure. However, that was not the case in my situation since the wiimote worked after restoring the NAND backup.

I had system menu 3.2 before uninstalling it, so I also had IOS 30 version 1040, not the stub. I did not uninstall it or install the stub. When I was about to reinstall IOS 30, Dop-IOS Mod verified that my wii had IOS 30 version 1040.

I bring this up mainly to get a better understanding of certain kinds of bricks. I may need to replicate the situation to test whether the system menu installation partly failed, but I doubt that this is the case unless there aren't any other possibilities. If I get around to doing it again, I will post my results.