Well darn. I just got a new computer too and the afterburners seem quite kaputzed for me as well.
After doing a fresh install of the SOTY edition (so it's stuck at version 1.20,) I hit the afterburners only to... well, not afterburn. There was the deadening clicking sound of exhausted afterburners as if I had just used all my afterburn reserves, yet my afterburner reserve was completely full. The ship didn't jump above max speed either. Oddly enough, when I'm below maximum speed, I can use the afterburning key to accelerate at a normal rate, but my reserves will not be used and I don't get the ever-pleasant jolt of an afterburn. I've also tried remapping keys and porting other pilots from the old machine and the condition remained unchanged.
It's rather depressing as this computer is only 26 hours old, hand built so no anti-FS2 technician had a chance to club the ol' game. As for the specs:
P4 2.8C
Asus P4P800 Deluxe
512MB PC3200 RAM
120GB HD
Radeon 9800 Non-Pro (but liberally overclocked; latest Catalyst drivers... 6.xx'ish)
XP Professional (SP1)
My computer that could run it was:
Celeron 433
384 PC100
10GB HD
Geforce 2 GTS
XP Professional (SP1)
And the compatability mode suggestion solved it. =) Thanks guys.