This happened a few times because I started to think I was imagining the part where I clicked the icon and saw the splash screen. So I would try to launch it again. It turns out that I am not going mad. FlashBuilder was really failing silently and just failing to launch. I tried deleting my workspace and launching again, but every time I did that it would recreate the workspace directory automatically and then fail to start.
Searching Google for "FlashBuilder won't start" yielded only one promising result but >the link was to a Jira defect that I can't see. I was about to call the professionals at ITFixed to have someone perform CPR on my machine when I figured I would try one last thing. Since FlashBuilder is basically Eclipse, I tried the old -clean command and like magic it came back to life.
Just open a command prompt to the directory where FlashBuilder is installed (On Vista: C:\Program Files (x86)\Adobe\Flash Builder Beta2) and execute the magic command:
I'm not quite sure what caused the problem in the first place. I had gotten a few out of memory errors (even though my machine has 4GB or RAM) but I can't say for sure that the problems are related.