Actually, what I was proposing was leave it on the right side, but rotate the pattern 90 degrees, so that it was a series of vertical stripes rather than horizontal. Then let it run down the right side repeating. And I have to agree with Dia, having the banner on both sides kind of renders the rest of the background irrelevant, since you can hardly see it behind the tables. I'd say leave the banner on the right side if you do anything with it, since you want it there to tug the eye across the page. Having it in both sides negates that benefit with the aforementioned added problem of obscuring what you assumedly intended to be the main element of the background (the stonework), while having it on the left side alone, while aesthetically it might look good, in terms of a web design wouldn't really achieve the desired effect. The natural position of the eye when a page loads tends to be near the top-left quadrant for most browsers, and anything on a text-heavy site like this that helps pull the eye to the right across the test always helps. That's an area that the current design is somewhat deficient in, admittedly, but it could work out well on your design.
As for getting it to work CSS-wise on your local machine, I can't say why it wouldn't be working for you, but if it comes down to it I can put it together from the final mockup. I know part of the reason you wanted to do this was to practice with CSS, but if you can't get it working on your own, at the least I could get it set up here and you could look over the end result.
I will give one general piece of advice as well, since it's a trap a lot of beginning designers fall into. You never want to design for a specific resolution when designing a webpage. You want to make a design that works at any reasonable resolution, because you can't guarantee what your end users will be using. These days reasonable would be defined by most designers as anything 800x600 or up. (Some go with 1024x768 or up, but if I remember correctly about 20-25% of internet users still use 800x600, so personally I'm reluctant to step it up.) Aspect ratio is also a consideration; since more and more people are using widescreen, you should try and make something that will look good in both 4:3 and 16:9, though this can be a tough challenge. Of course, a lot of people using widescreen don't use maximized browsers either, so you can't even count on aspect ratio too much.
Anyway, the best way to do this is to design things to float. Elements should be able to shift on the page as the browser window changes size, and background elements should rarely be a page-filling image. A repeating image is okay, as those are easy to work with for any resolution size, as is a background element that fills a part of the screen, such as a watermarked background image on one side of the page. I can understand why you were looking towards 1024x768, since it's the most common resolution currently used by internet users, and it's only sensible to work for the most common case. But in this sort of situation, there are so many users not using the most common case that by focusing on that, you actually end up excluding the majority of users (I believe 1024x768 is something like 40% or so). Especially with, like I mentioned, the rising proliferation of widescreen monitors. At least half of monitors being sold today are widescreen, and though 4:3 is still the most common in use, the user share is slowly tipping in favor of 16:9.