Here we go!
Q1: Mod-chips make your Wii stop working.
A1: Let me start by explaining something essential about the Wii mod-chips. In normal circumstances (without a mod-chip installed) when you insert a disc (GameCube or Wii game) in the console then the disc-drive will read the data on that disc and sends that data to the Wii motherboard, the actual console! If you put a copied game in the drive then the disc-drive simply 'recognise' this burned disc and refuses to read the data. It will send a message to the motherboard telling that 'he can't read the inserted disc', and the motherboard simply repeats this message on the screen.
Now we install a mod-chip on the disc drive. The mod-chip alters the behaviour of the disc drive (that is why people call it a drive-chip) and causes it to accept written media (burned disc). The mod-chip basically 'fools' the disc drive or instructs the drive to read what is on that disc no matter if it is burned or not. And so the disc drive goes to work. It reads the data and sends it to the motherboard. The mother board can't tell the difference between data that comes from a burned disc or a manufactured disc. It simply processes the data that is coming from the disc drive and therefor the Wii console can't ever know that a mod-chip is installed or not! This is called 'stealth' mode.
Since the Wii doesn't know there is a mod-chip on board it is impossible for it to make the Wii stop working because of it. However in the past there were a few issues that caused your Wii to be 'bricked'. But that was not because it 'recognised a mod-chip'.
Q2: What is a 'bricked' Wii?
A2: If your Wii is bricked then it means that the software in your Wii (the operating system) is stuck in an invalid operation. This means that all your hardware is fine and the actual Wii is not damaged! It is simply a software problem that can ONLY be resolved by Nintendo. Basically a bricked Wii won't work anymore. At all!
Q3: So how did the Wii got bricked then? (The famous Super Paper Mario issue).
A3: As you know the Wii is released worldwide in different regions. There is one for the Japanese market (the J-NTSC), the USA Market (U-NTSC) and the European/Australian market (PAL). NTSC and PAL are different types of producing graphics on televisions and monitors. If you have a NTSC Wii then you won't be able to play PAL games on it. But as soon as you instal a mod-chip you WILL be able to play most games from all regions on your Wii no matter what region!
A few months ago Nintendo released a game called Super Paper Mario for the NTSC consoles. But the PAL Wii's needed to wait for quite some months to get that game! (It has been released now for PAL too). So a few people that had their PAL Wii mod-chipped decided to burn the NTSC version of the game and play that one.
On the game disc, there was a new firmware update for the Wii console. If you insert the disc then a window would appear telling you to update the Wii console. The Game needs this update in order to play. But the update supplied on that disc is an NTSC update for NTSC Wii's! Some people updated this NTSC update on their PAL Wii, something that wouldn't ever be possible on a Wii without mod-chip because the console would simply reject the NTSC disc.
As you can guess, those PAL Wii's didn't like the NTSC update and got bricked because of it.