I figured out a way to launch the IDE from command line and capture some debug information from the Java runtime.
Execute this command line from the folder where the arduino.exe file is installed:
"C:\arduino\arduino-1.0\java\bin\java.exe" -verbose -Xms128m -Xmx128m -classpath "lib;C:\arduino\arduino-1.0\java\lib\tools.jar;lib\pde.jar;lib\core.jar;lib\jna.jar;lib\ecj.jar;lib\RXTXcomm.jar" processing.app.Base
You will see a bunch of information in the console window. Hopefully this will help narrow down the cause of the problem.