You don’t have to look far to find ID articles supporting the claim that the vast majority of the human genome has function (e.g. here). At the same time, there are ID articles claiming that function is exceedingly rare in DNA sequence space. That is, there are a very limited number of DNA sequences that can have function.
These two concepts are in serious contradiction to each other. Whatever your feelings are towards the ENCODE study or similar research, there is one unavoidable fact: the vast majority of the human genome is accumulating mutations at a rate consistent with neutral drift. This is true if you compare just human genomes or compare genomes between multiple species. This means that there is a lack of selection against deleterious mutations in the vast majority of the human genome. This can mean one of two things: 1) the function in those stretches of DNA are not affected by changes at any base within that DNA, or 2) the vast majority of the human genome does not have function that is being selected for (what ID supporters and creationists would call microevolution).
If we accept the ID claim that these sections of DNA have function then it leads to the unavoidable conclusion that function is found in almost any DNA sequence. Function is not rare in DNA sequence space. Instead, function is found in almost every random DNA sequence, and no mutation can do away with that function.
As far as I can see, ID has to pick between “no junk DNA” and “function is rare”. They can’t have both.