Slicesoul has been the closest in his recommendations so far but his recommended equipment is a little to high-end to fit your budget. Its clear to me that the people who keep recommending core 2 duos haven't been following FSX developments closely, and have instead based their recommendations on general core 2 duo supremacy. I think its great they are trying to help but I know you can do better than an E6600.
The Microsoft Aces Team (group respobsible for FSX development) have been blogging about FSX enhancements in the upcoming service pack release. Phil Taylor (Aces Team lead) has said that the SP1 patch will essentially take advantage of multiple cores and people will see a performance increase from having a quad core. Essentially, FSX will become multi-threaded in the SP1 update. The SP1 patch isn't released yet so we don't know the true impact of the multi-threading on a quad core. Based on the significant performance increase in other multi-threaded applications, however, a quad core may have a huge impact on FSX. SP1 was supposed to be released in late April, but they encountered some problems in Beta 3 and they have pushed back release until May.
After they finish SP1, the ACES team will start working on the DX10 patch for FSX. They hope that can be done in September. Although Phil Taylor is loathe to recommend any specific hardware, he did make an off the cuff statement that seems to favor the ATI DX10 solution. He said something to the effect that DX10 might be harder to implement because of the different approaches taken by ATI and NVIDIA and trying to figure out why ATIs geometry shaders were so much better than NVIDIA.
So, for a new computer under $1500 to run FSX, you should definitley aim for a budget quad core processor and then the best DX10 card you can buy. The Q6600 keeps falling in price and is a reasonable $550.00. If the ATI 2900 XT is as good as it seems, and is in the $400.00 price range, than that might be a good option for a video card. You can get some good RAM for $200.00. That leaves you $350.00. I don't know what other components for the computer you already have, but I would invest in a good motherboard and power supply before I messed with anything else. A good budget mother board is the Gigabyte P965 DS3 and the Corsair HX620 PSU has gotten great reviews everytime a professional evaluator has touched it (thought its pricey).
The main thing is getting the Quad Core processor and the best DX10 card you can afford after that. Happy simming!
Rob