Yes, it is definitely possible to build a PC at 14
This must be true as i have done it and the PC works (did i mention that my arm was in a sling at the time)...... This was about a month or 2 ago and i'm 14 at the moment.
Just dont go out and buy any old compatible components, spend a LOT of time doing research...boring i know, but i did it.
The hardest thing about doing it at our age is budget (i'm not as rich as i'd like to be.... but then again, who is?), you can get a decent(ish) PC for about £350, if (you overclock it a lot...) you don't need to run Doom3 at full reseloution and so on, but it would be running linux... (if you need windows get win98SE cheap)
Anyway - Good luck