According to one of my proffessors, music is defined as an organized and deliberate sound, and an instrument is something that will implement an organized and deliberate sound. So according to raw definition and facts, yes the PC is an instrument.
Trance is far from the only music that is made with computers. Many contemporary classical pieces written for the symphony incorporate synthesizers as well as pop, hip hop, rap, country, you name it, they've all used some type of computer or digital remasterring either within the song itself or post recording.
If you study the history of music you will see that the progress within the music coincides with the progress of society. For example, the classical period happened around the same time as the printing press and because of this, music was written at an easier level and made more accessible to the general public. Like mentioned earlier, the computer was invented by people just like the printing press, and is no different than any other technological advance including the invention of the fortepiano and the saxaphone. The fact that it uses electricity has no affect on whether or not is an instrument.
Aphex Twin makes very complicated and abstract music using different electronic techniques. I highly recommend them to anyone who is interested in creative synthesizer techniques.