Rules lawyering and loophole-seeking aside, immunity to fear effects = immunity to Intimidate. Period.
Cast a Fear spell at a Vampire:
"Muahaha! Silly mortal, I am immune to your pathetic attempts to invoke fear!"
...Fighter then rolls an Intimidate check...
"Oh please mighty warrior, stop glowering at me, it's making me ever so nervous!"
...yeah...
That's not how I see it at all.
The wizard casts fear, reminding the Vampire of the madness and horror which dwells only in nightmares.
"Silly mortal, that's the stuff I'm made of."
The fighter rolls an intimidate check, reminding him with words that his fists can smash boulders.
"On second thought, I don't want to die. Carry on, adventures."
But, fine, I give up. I'm only human and can take so much. Most people arguing against me don't want to tell me why the entry in Monster Manual IV doesn't hold authority or explain how I'm interpreting it incorrectly. I ask myself: what's the point of sharing an opinion when nobody wishes to examine it? I ask others: what's the point of having an opinion if you'll never let it be argued? If rules lawyering is so horrible, let all rules be decided by the person who argues the longest. I will not be that person, however, I believe you know the type of person that will tend to be.
Here was my full train of thought from the beginning so that I can wash my hands of this thread. I read the SRD for the rules on undead creatures, found it vague, but clear enough to say "undead cannot be intimidated." At which point I turned to Libris Mortis as the definitive source for 3.5 undead creatures, if it said no differently or said nothing at all, then I would take the stance of non-intimidation. Libris Mortis contained no valuable information on intelligent undead creatures but a peculiar wording of undead type. I checked all editions of the Monster Manuals I had, in reverse order, until I could find wording that matched Libris Mortis. Monster Manual IV was a hit and the wording was not a blanket statement like SRD. Assuming that because the wording was not a blanket statement, it was the intent of the authors that SOME form of mind-affecting effects could work. With rather vague wording, I made an assumption that ability could only refer to special ability as per literal definition, it wouldn't make sense that undead are "Immune to mind-affecting strength, dexterity, constitution, intelligence, wisdom, and charisma scores." At which point, I decided to change my stance to one that supported intimidation, once unable to find evidence against it, I put it forth to the community as a theory.