Today the capacitors for my Game Gears arrived. Though only two of the three Game Gears I ordered have arrived at my house by now I was willing to give this whole repair thing a shot. Well at least I was willing to drop by a friend's house who's also into video game collecting and had a more or less faulty Game Gear himself. Thing is that he really knows his way around soldering stuff so basically I let him handle the difficult stuff and I am grateful he did this for me. After he switched the capacitors on the first Game Gear I was pretty depressed because the damn thing still turned off once I cranked up the brightness to about half of what should be possible - big downer there. The sound board worked however.
After that he continued with his own Game Gear and luckily everything worked out for the best. The sound on the speaker was nice and loud again, the same with the headphone plug and the viewing angle problem was fixed, too. After that my second faulty device followed and again everything worked flawlessly once he was finished. The soldering took about 45min to 60min for each device and prior knowledge of the Game Gears motherboard wasn't really necessary. I bought the spare parts on ebay for 4GBP per capacitor kit including a manual (which like I said wasn't really necessary).  
So if you have a Game Gear that doesn't play sounds anymore or doesn't even start anymore it's pretty likely that you will be able to fix it. If you live in the UK (which I don't) it's even easier. There is a guy on ebay who offers complete capacitor swaps and cleaning for just 11GBP. If you don't live in the UK it still shouldn't be a big deal. If you ever held a soldering iron in your hand you can do it and if you haven't let someone more experience teach you or have a friend doing it for you. It's not much of an effort to make this thing like new. By the way faulty Game Gears cost like one or two bucks on ebay. 
In the next few days I will check out the games I bought so far and the once that I am about to buy. I guess I will blog again soon with more about my Game Gear experiences.