I would strongly recommend you to avoid FSX with such an old computer.
I wouldnt say that. I run FSX on quite an old machine myself. P4 3.0, 1gig ram, pci 512mb graphics card, and 500gig hd. Now I will tell you this... I run with most of my settings very high, and get up to about 10fps depending on the location, and even the aircraft. If I lowered the settings a bit, I could get some good framerates. Not like the quad core type framerates... but considering my comp specs, its pretty good. The key for me was Nick's tuning.
Of course, you can run it.
But the lack of CPU power will prevent you from enjoying addons. You won't be able to get crisp ground textures (blurries), you won't be able to enjoy a precise mesh, you won't be able to push the autogen or the water settings, and you will not be able to enjoy a complex plane or scenery.
I know this because when I first tried FSX, my computer was an old PIV 3,2GHz with a 6800GT video card. I could get an interesting graphic quality, but only when flying very slow planes. I had to kill the water effects, limit the weather, limit the autogen and limit the ground textures to 5 meters, I had no AI traffic and flying anything faster than the default glider was excluded...
With such restrictions, I would really advise somebody to buy a cheap FS9 (on the net or in a local store, if you can still find it) instead of waisting his money in FSX, don't you think ?