Ok, I have a machine that is somewhat similar to yours:
P4 3.0 w/HT
1 GB ddr-400
7800 GS (AGP)
Firstly, you should be using Detonator drivers with that ancient video card, NOT Forceware. Would be much preferable that you upgrade it, but AGP cards are hard to come by anymore. Secondly, you should be using a FRESH install off the CD, and using the Eidos 1.02 patch with Nvidia TNT selected, NOT Riva 128. If you are trying to use some Ultima edition, you are screwed, because it CANNOT be properly patched. Thirdly, Aali's graphic's patch can be applied.. AFTER you configure the sound and graphics in the FF7 Config program. Don't forget to install the registry modifier, and set the FF7.exe to "98/ME compatiablity".
If you have to re-set something in the FF7 Config, you will need to re-install the FF7 Registry hack for Aali's program to work