That's one way I thought of, but it's not very eloquent and then you have the spasms when it's running into a wall.
You could use 4 "sprites" that are updated to the sides of the box every tick. When one overlaps the box, whichever direction is hitting you cant go.
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So is there no way to just check if "Sprite.X + (200*TimeDelta) is collision-free"?
This may be what you're looking for, hopefully:
http://upload.namelezz.net/downloader.php?file=3828287_perfectstop_002.cap
I have never heard of .Left and .Right, what are they exactly?
So it's what you're looking for, yay!
Basically Sprite.Left would be the X coordinate of the left edge of the object, Sprite.Right the X coordinate of the right edge obviously.
Try this:
http://theone.lithfaq.com/blocker2.zip
invert an overlapping at offset.