Hey Drew.

The easiest thing is to just make a read-only view.
Create a new view.
Copy all of the controls from the main view to it.
If you have 2007, open the view propoerties and set to read-only.
For 2003 switch your controls to expressions or make controls readonly
individually.
Then add a field which is called status.
When they submit set status to submitted and switch to the readonly view.
Put a rule on open that is status = submitte switch to readonly view.

That is it.