I have two that I consider my "worst".
The first was a dell dimension tower, fairly plain specs that wouldn't power on/stay powered on. The customer said that it was a web server that they keep in their basement, so they needed it back quickly. On the outside, the system looked fairly normal, a little dirty. When I took the side panel off, several INCHES of dust/sand fell out of the system. My boss at the time had me clean it despite the fact that the components were literally buried and a new computer (and filtration system was in order). Amazingly enough, after cleaning, it worked fine somehow. I think I may still have pictures somewhere....
The second was a typical cat pee computer. Of course, it smelled awful, some cards were fried, and it was our policy to either pack it up and send it home or require it be cleaned and every pee'd on part be replaced. The reason the system's in my worst list is because the customer ended up being an uncle I hadn't heard from in years...