A science building encounter had a mi-go appear and stated I could not use investigator cards if I failed a speed check. What does this mean?
Investigator cards are explained in the Arkham Horror rulebook.
They are briefly mentioned on page 2 under Game Components and Preparation, and are covered in more detail on page 3 under Investigator Cards:
The small cards included in Arkham Horror are called investigator cards. They represent useful allies the investigators may meet and items they may acquire during the course of the game. There are six types of investigator cards
The specific cards that fall under this category (in the base game) are:
- Common Items
- Unique Items
- Silver Twilight Membership
- Bank Loans
- Blessings & Curses
- Deputy of Arkham cards
Expansions also add their own additional Investigator Cards, such as Injury & Madness cards in Dunwich Horror.
This does point out a specific lack of clarification in the rules that is not covered in the FAQ as far as I can see: If Curse, Injury, Madness and other detrimental statuses are also Investigator Cards, then by definition of the Science Building encounter in question they could also not be used. This would then present the potential for the encounter with the Mi-Go to become easier for some investigators. (If you chose to play it strictly by the wording of the card as-is. Personally, I would use the implied intent of the card, which is that beneficial Investigator Cards could not be used.)