Okay, I'll start off by simply saying that this completely eludes me. I've built a lot of other websites, but this one just... Kicks my butt.

I have a webpage with a background set in CSS. On the page, I'd like to have a DIV with a semi-transparent white background(maybe at opacity 40%). However, I've found that the only thing that half-works, is something that also changes the opacity of the text. The only thing I want to change, is the background.

I bet you're thinking, "Well, just edit the background in that one part with a layer in Photoshop or PaintShop Pro, and then use it that way." But the thing is, I want to make this look nice for all possible screen resolutions. If I were to take the background and edit it to look good on my resolution, which is 1024 x 768, it would NOT look good on an 800 x 600 resolution.

Does anyone have any suggestions or solutions?

The methods you mentioned are the only ways to get that effect :P You could try making two separate divs, same size, placed in the same spot, one with the translucent background and the other on top with the text in it.