What is the biblical basis for Dispensational Premillennialism? Related:
  
  
  What are the differences between the different millenialisms?
  What is the biblical basis for Historical Premillennialism?
  


Dispensational Premillennialism is a view of the end times that (very, very basically) says that Christ will return to rapture believers, then there will be a tribulation, then the millennium. (something like that. Disp. Premils: please edit. Also, see Caleb's answer on the above related question)

What is the biblical basis for this belief? Also, what logical deductions that support this belief can you make from biblical passages? 

If tradition can be a convincing argument, feel free to use it.
This question should probably be answered by somebody that believes in dispensationalism as well. (Obviously, from that sentence you all know that I do not.) Nevertheless I will venture a "pre-answer". I will not discuss passages of scripture, that taken together might be understood as supporting the view.

I'd like to put some focus on the hermeneutics behind this view. How do you read the Bible in order to come up with this specific interpretation? I think the following points apply:


Unless there is a compelling reason to interpret a passage differently, all scripture should be read literally. The question of genre is not high on the agenda. When reading texts about eschatology in the Bible, they are all considered a topic, not a genre. 
Thus, there exist no specific apocalyptic genre that needs special consideration. The question what the texts in Revelations, Daniel, Ezekiel, etc meant to the original hearers is therefore low on the agenda. Instead all focus is on how we today can harmonize various sayings in different passages having access to the finished Bible.
Specifically, numbers telling passage of time are to be understood literally. Saying that a number only has a symbolic meaning is out of the question. 
When there is a possible difference between various passages in the scripture, the main solution is not to re-interpret the passage as such, but to apply them in different phases. Thus the second coming is a 2-phase event, all time, including the Old Testament time, is divided in different "dispensations" during which God uses partly different means to help mankind.
The "natural Israel" is of utmost importance when God is shaping history. The church age is basically just a phase. It's importance is primarily in preaching the Gospel to the ends of the earth. For the salvation of the individual, this is of course very important, but it is not really important for God's rule of the earth.


Using this hermeneutic approach one can dive in at various places in the Bible to explain Dispensational Premillennialism, since the teaching relies on how to fit different parts of the Bible together. The Bible read this way is (among other things) a puzzle and the pre-trib view is its solution.

(Yes, my bias does show through in this answer. I hope, however, that it does not mean I have explained anything in a false way. I have read substantial amounts of text written by pre-trib theologians.)