I'm sorry if this comes across as a rant.
Digidesign are not being awkward - they have been quite upfront about which computers they support, which are fully tested etc. I agree that there are not that many tested and qualified machines, however Pro Tools is not your average run of the mill programme.
It is very closely integrated with the hardware, meaning that if there is an incompatibility it can be fatal to the programme.
I'm going to guess that you have an AMD K2 or AMD X2 processor? If this is the case, then the problem is that AMD claim that these processors are SSE (
Wiki page) compliant, when in fact they are not. Not Digidesign's fault. Further if you in fact have one of the processors listed as incompatible, well then that's not their fault either.
As always I very strongly recommend sticking with one of their qualified machines, whether this is a Mac, or one of the Dell/HP workstations. Yes they cost a fair amount of money - but if you are serious about using Pro Tools it's a sound investment. If you're not all that serious about using Pro Tools, I'd recommend looking into Cubase.
Sorry to sound like a school master launching into rhetoric, I don't mean to offend.
So a couple of questions if I may...
What is your budget for a computer, and what are your requirements?