Microsoft Flight Simulator 2004 honestly doesn't need one heck of a system to run at all. Looking at the specs, it looks like it can be ran on my 10 year old Dell Inspiron 3800GT laptop, and also looks like something my gaming computer would overload. If anything, any laptop with a decent video card should run it, but I'd shoot at a system with 2GB of RAM, a decent nVidia/ATi card, and a high RPM S-ATA drive, and a good dual core processor.
But if anything, I wouldn't shoot for a laptop geared at the minimum requirements. If you can, a system at or above the recommended specs would be best. Also, considering what you might be playing in the future can and should be a factor. Otherwise, I'll see what I can find. I'm almost positive I'm not going to find any 9800M GT cards or even Radeon 3870s in SLi/Crossfire for your budget. However there is a chance that I may.
EDIT: Right now in searching, the cheapest system with a 9800M GT is starting at $1,300, certainly over your budget. This was from HP. I did find a system with an 8600M in it that was under your budget though. Let me check VAIO now...
EDIT2: VAIO seems to have some pretty good systems there as well. The only systems I can find under your budget all have Intel Media Accelerator cards though. If you want me to check out other brands, I can do that.