I'm making a website, and it's all centerised (it's not big enough to stretch across the whole page). As a result, the position I want my top-layer textbox to be is different in 800*600 as it is in other resolutions.

Is there any way to define where you want the textbox to be, measuring it in pixels away from the center of the page?

With pixels it will change with each resolution, so there's no way to 'centre' and position absolutely at the same time.
For a different CSS way...
Remove all absolute positioning codes. To the body CSS section add text-align: center;. To each image/div on the page add margin: 0 auto;
Depending on how your page is set up you may need to do a few other tweaks to make it look right... or just resort to using tables.