First off, the first time you start Firefox, it will take a little longer than usual because it starts up the import wizard which gives you the option of bringing in IE settings. For reasons I've never been able to figure out, there isn't always a corresponding entry for this on the task bar. So check for the presense of this by minimizing windows one by one until you get to the desktop.
Another possibility, is that usually once in a blue moon, a Firefox process will turn zombie. Which means it's not doing anything, but it's still there (or it's undead). Fire up the task manager, and check the process list. If you have multiple Firefox entries, you'll need to kill each of them before you try launching it again. Otherwise you just add another zombie process to the list.
And as usual, after using IE, you should always be sure to scan your system for spyware which may be having undesired interactions with the Firefox process.