If you disturb a Jenga block, can you push it back into place?
According to the official 2000 version of the rules:


  As play proceeds and the weight of the tower shifts, some blocks become looser than others and are easier to remove. You can touch other blocks to find a loose one — but if you move a block out of place, you must fix it (using one hand only) before touching another block.


Since this rule includes the proviso before touching another block I take this to mean that you can't touch blocks after you have started to remove your block.

I believe it would be within the spirit of the rules that you could try and replace the block you started to remove, then try and remove the block you disturbed. 

The key is that you can only touch one block at a time with only one hand.