Dividing a rectangle into 4 parts in the ratio 1:2:3:4, with only 2 lines

First, divide the rectangle equally on its long side, as suggested in the comments. In the left rectangle, mark the point that is $\frac45$ of the way up and centred horizontally; do the same for the right rectangle, but mark the point only $\frac35$ of the way up. Then draw the line connecting the two marked points. Since this line crosses the left and right edges of the whole rectangle, the four small triangles shown above (bounded between the purple and darker grey lines) have equal area, so the left rectangle is divided 1:4 and the right rectangle divided 2:3. Overall, the rectangle has been divided into four parts with ratio 1:2:3:4.

This solution does not require moving the pieces as in Donald Splutterwit's answer.

An alternative solution very similar to Parcly's (image lovingly created in Excel):

You need to move the two pieces into the right positions before you perform the second chop.