For many builds now stretching back to the early 7.0 EAP releases, only M2 has launched from the desktop icon. No other builds did, and the current release candidates do not either.
It does run from idea.bat if JDK_HOME is set suitably.
I traced this to idea.exe failing to run. From a Cygwin command window:
Brian@EROS /C/Program Files/JetBrains/IntelliJ IDEA 7323/bin
$ ./idea.exe
[YourKit Java Profiler 7.0.2] Using JVMTI (1.6.0_02-b06;Sun Microsystems Inc.;mixed mode, sharing;Windows;32 bit JVM)
Error occurred during initialization of VM
java/lang/ClassNotFoundException: error in opening JAR file ..\lib\boot.jar
Brian@EROS /C/Program Files/JetBrains/IntelliJ IDEA 7323/bin
$ dir ../lib/boot.jar
../lib/boot.jar*