Is that P-4 3.4G a Northwood cpu or a Prescott cpu? You might have a one of the higher P4's that have H/T; hyper-threading. With a single core P-4 that has hyper-threading(H/T) you can run the game and get about a 1300ish score with a low end graphics card. You will also need a OS that supports hyper-threading. I use XP Pro.
I've tried to run the benchmark on a lot different low-end video cards like yours. In fact, I tried to run it on a 7800 GTX and a 7900 GS. The 7800 is a 256 meg and the 7900 is a 256 meg. Neither will produce anything but a black screen, some sound, and a benchmark low score number. Makes no difference what driver version I use, still get just a black screen.
The machine I use to run the benchmark and play the open beta is similar to yours:
P-4 3.2G @ 3.55G Extreme Edition with H/T 2mb level 3 cache socket 478 . . . this is a hybrid Xeon Processor(Gallatin)
ASUS P4C800e Deluxe motherboard. BIOS 10.14 most stable for overclocking with LL ram.
Radeon HD 3850 AGP 512mb 256 bit bus. 10.9 driver with ATI tools.
Corsair XMS DDR 400 2x 1G ram LL ram @ 220.127.116.11 on a 1:1 FSB of 16x220. Get a drop in performance using 3 gigs.
Thermaltake 560 watt psu. 320 watts on 12v and 240 for the other rail. Not enough juice for old systems and newer video cards and 3.5 gigs of ram, all the other cards and drives really take this psu to task. I'm sure it's nearing MTB so there will be a loss in efficiency.
OS is Windows XP Proffesional SP3
It's a seven year old system. It runs all the newer games just fine. SC2, Crysis, etc. It really chokes on FFXIV.
I've scored as high as 1500 ish with a 3.7g overclock but the game is still not playable with other ppl on the screen. That blue crystal area, crowds in the cities turn this game into a slide show. 12-15 fps around the blue crystal and inside the cities. Other places, 25-30 fps which is playable. The UI lag is unbearable. It takes way too long to use the menus. The only thing you can really do is fish. No problems with fishing at all. You can also turn all effects on high and take some incredible screenshots.
With this system, the game is unplayable. If you choose to upgrade your video card, if your processor has hyperthreading, if you OS supports HT, if your parts are exceptionally good (old) parts, you might give it a try. If not, do like me and just keep playing FFXI, SC2, Halo, etc.
FFXIV is a game for high end systems.