Have the same problem myself, installed the lastest drivers (geforce fx5500 256mb) and get the same error message. I hope I fair better with the retail game I have on order. Trying to enjoy the Beta is a loss cause.
Your video card is below min requirements as well (Video: NVIDIA GeForce 7950 / ATI Radeon X1800 / Intel HD Graphics ). The Beta game program and the retail game program are almost the same (definitely the engine will be). What I mean is that if you cannot run the beta client, you probably won't be able to run the retail one.
If your other hardware meets the minimum requirements, you might be able to upgrade your video card, as was suggested in this thread.
Either one of the two links I posted will run STO. They are not top of the line cards now but they will at least let you run the game on medium specs.
And if you can upgrade your current cpu you can find some good deals at the same websites also.
Both these video cards are PCI-E the original poster's computer uses AGP card.
or to put it another way. the two video card listed on those links will not go (FIT) in that computers video slot.