I'm sure drothgery has gotten to check out his ECS for Investigate by now, but here's a quick summary for future reference (and my take on it, so drothgery can correct me if he thinks it should work differently):
The Investigate feat (ECS, pp. 55-56) enables new uses for the Search skill--finding and analyzing clues. Clues are described specifically as being "physical, and can be seen, heard, touched, smelled, or tasted. A clue stands out because it is not a normal feature of the area being searched." Examples given are: a trampled flowerbed, a broken urn, a pin snapped off in a lock, a torn strip of cloak, a burnt scrap of scroll, or a brooch clutched in a dead man's fist.
If there are no clues that can be found, a successful use of Investigate doesn't turn anything up.
The base Search DC to find a clue (if there
is a clue, now--this doesn't cons things up out of the ether) is 10, modified based on how disturbed the area being searched has been. +0 for an undisturbed location, +5 for a disturbed location (slightly and perhaps unintentionally. A good classical example would be bystanders walking around on a crime scene), and +10 for greatly disturbed (massively and intentionally--scrubbing down the area, etc.)
Once a clue has been found, analyzing it requires a second DC 15 Search check. "By examining a body, you might determine whether the victim fought back or provided no struggle at all, or if claws, a weapon, or a spell killed the victim. By looking at a scorch mark on a wall, you might approximate the position of the spellcaster when the spell was cast."
The Search check to analyze a clue is modified by the circumstance, and how significant the insight provided by the clue is. The Search DC is increased by +2 for each day that's passed since the event in question (max +10), +0 if it's a minor clue (provides only a small piece of the solution), +2 for a moderate clue (provides significant data toward the solution of the puzzle and could lead to a conclusion without additional data), and +5 for a major clue (provides everything the investigator needs to solve a puzzle, although the solution may not be immediately obvious.)
A really good example that springs to mind of how these two things work together is a classic Sherlock Holmes snippet: Holmes notices that Watson's shoes are stained by a certain color of mud (find a clue). He then deduces that Watson has been to a specific part of town where new construction is happening, because it's spreading a lot of dirt about, of that specific hue (analyze it.) Holmes does this all as a free action, which clearly implies that Holmes is an epic character. *cough*
For this specific case, I'm not sure whether Investigate even applies. I'm thinking in terms of the puzzle in question being why the fiends wanted Lord Alistair. An example of clues in the recent posting might be the drawings and journals. Analysis might be able to suggest what he was working on when the fiends came in, or perhaps provide some insight into what Lord Alistair's research was trending towards: Hariel probably wouldn't know about fiends in detail, but she might be able to deduce from the pattern of the research that some item is of greater significance, and draw that item to the attention of the people who do know more about fiends.
Investigate might also reveal as character knowledge some of the "what's going on" bits that were posted about how the fight came to be, with the silence spell to try to keep Kahlia from getting involved, etc.
Investigate is definitely one of those skills where it's totally up to the DM what information may or may not be gained from use, and how to provide that information. Sometimes, there won't be any use for it. Sometimes, it'll be an appropriate time to use it, but there still won't be anything useful to be gained. (Same sort of thing as Gather Information: sometimes there are no locals to talk to. Sometimes there are locals, but they don't know anything of import.)