So I'm stuck at this part:
http://image.com.com/gamespot/images/2003/reviews/589721_20031209_790screen018.jpg
I've got to both to the sand cloud and the box. Pushed the box into water and am clueless as to what to do next. Could anyone help, spoiling the game as little as possible?
Do I have to use the box in this part to exit the level somehow?
Need I go back to where I came from?

So, you got the box ? You pushed to the wall on the right to climb up and get sand cloud. Now continue on your right, climb and go along the wall around the corner. Jump on the other side. Continue to the beam and balance over it, stop in the middle so you can reach the rope on your right side. Jump. Now balance to reach the next and so on. Attached pics, my explanation may not be really clear ;)

Thanks a lot for the in-depth walkthrough, Pops! :D
Frankly, I did all that, too, before writing the message.
I loaded the same savegame again to check if I missed something, and am stuck once again. I did swing on all the ropes and got to the part where you enter a dream (?) and drink from a fountain, increasing your health.

LOL, the way you took was optional infact. The bright light beam marks the exit, you would just have to climb up the rope.
So after the dream just go back, and jump over to the rope again. Then simply climb up. I understand that part can be quite confusing. I've played the game so many times, I could play it with eyes closed now. I still enjoy it thoroughly, it doesn't get boring.
Also, prepare for combat ;)

Don't feel stupid. It wasn't that obvioius (though the "show the way sequence" at the beginning of the level indicated it to be the exit). I was stuck there too on my first playthrough ;)