The switches linked by aholtzma look good; you probably want an on-off-on switch for your power swtich, and an on-on switch for your polarity switch. I would guess that the glue and black rubbery stuff you're complaining about is a sealant that they use to make the subwoofer enclosure airtight to improve the sound quality and keep things from rattling when the sub is in use. As for the original problem, the component that tends to fail most often is capacitors; do yours have any bulging or discoloration?
I got one of these for Christmas, so I can confirm that it works on linux. It looks like someone is working on a linux driver, but it's in the very early stages of development. They're hosting it on github: http://github.com/cosmonaut/xf86-input-magicmouse
it's a bit hard to understand what you're saying, but it sounds like you're trying to replace the screen on your MacBook Air, and aren't able to see anything on the screen. My best guess is that the backlight isn't turning on for some reason. I can see two possible causes for this: 1) it isn't plugged in, or 2) it's broken. I'd check for (1) first, and if that doesn't work, it's probable that you have a faulty backlight. I've found that I can see my laptop screen in bright, direct sunlight, even with the backlight off, so you might try shining a really bright light at it when the laptop is on, to see if the screen is working, even if the backlight isn't. If you have removed the back from the LCD, you could also try shining a light at the back of the LCD to see if you can see anything.
I agree with Chris, it sounds like re-applying the thermal paste on the graphics card is probably the best thing to try. Failing that, I would probably install Linux on it and use it as a headless server, maybe as a home file server. Laptops generally make nice servers because they draw relatively little power, and have a built-in battery backup. If you're looking for something creative and relatively easy to do, you could install linux, install MPD (http://sourceforge.net/projects/musicpd/), load it up with music and attach it to your stereo for use as a network-attached jukebox. I've found Theremin (https://theremin.sigterm.eu/) to be a really nice MPD client for OS X. There are graphical and command-line clients available for most operating systems, and even clients for the iPhone/iPod touch and other smartphones.
The bottom line is that your computer needs to know where to go to resolve DNS names. You can set this in several ways: 1) Configure your computer to use a static DNS server all the time. This should work regardless of where you are (unless the network admin is a real BOFH) 2) Configure your DHCP server to hand out the proper DNS server as part of the network configuration. For almost everyone, this just means configuring your router with the proper DNS server. Then, every computer on your home network should use this DNS server.
When taking apart laptops, I find that the designers put case screws in some pretty funny places. I recommend taking off things like the cover for the RAM, and looking under it for case screws. I'd also look under the battery and inside the battery compartment, they like to hide the case screws in there. In general, I've found that, when the case won't come apart with light pressure, there's usually a screw somewhere nearby that I missed. I've also found that some laptops open from the top, like my roommate's dell and my old, and others open from the bottom, like the new MBP Unibody. Maybe turn yours over and try from the other side?
A roommate of mine had a similar problem. It turned out that replacing the inverter fixed the problem. My best guess is that the inverter functions ok when at full power, but flickers when trying to deliver reduced brightness (as happens when the laptop is idle for a while). My roommate and I were able to duplicate this by turning down the brightness, which caused the display to flicker more.