Thanks for correcting my info. Couldn't think of 'PS2' and I wasn't 100% sure it was a standard PS2.
If I were so inclined, I'd take the free vulch bet though dedalos. Without the throttle attached to the PC, the stick has no means of connecting to the PC (the PS2 cable is the only cable on the stick, and it goes from the stick to the throttle, then the USB connector goes from the throttle to the PC) ergo it's gonna be mighty, mighty difficult for the PC to recognize the stick without the throttle plugged in.

Bighorn and Morfiend have got the right of it. If it were me, I'd buy a new cable, see if that fixes it and if not, then pursue warranty.
Wiley.