Spoiler
Do you need the ID card? The answer is: Yes, but not now.
There is another way of getting to the second floor apart from using the elevator (which you can't because you don't have a card)...
Go to the room with lots of crates everywhere (note the cargo lift in the down-left corner and the computer thingy), use computer, fiddle around for a while, exit computer, speak to the man in that room... etc... then you should figure out what to do