My grandfather was a 20-year Air Force veteran who often built computers. When I was a child, I asked him for one, he told me that if I wanted a computer, I had to build it myself. He gave a bunch of parts with a few empty towers and I was told to figure it out if I want it.
I managed to put it together and the BIOs loaded up, but I had no way of installing an operating system. Because I finished building it, he came over, looked it over, and then took out what he said was a Windows XP military installation CD he was given. He showed me how to install it and I had my first computer!
I told someone about this a couple of years ago and they said he was "too harsh" for telling me to build a computer with no instructions. However, I agreed with my grandfather's approach and I was thankful for the opportunity as he did not have to give me the parts to build one in the first place, and the experience of building it made it more special.
To answer your question, the first computer I had was custom built by me.