My intelligent key is stuck in the car key port and the dealer is closed today....The key was inserted by mistake in the key port without its black cover :-(Will it drain down the battery or do any damage?

I honestly dont know how it got stuck, unless you forced it in backwards or upside down. in that case, you kinda have to yank it out. It should only be there when the battery dies... it wont drain the battery, and damage may be avoided if removed smartly

I tried pulling it out but it doesn't seem to come out :-(

The key is finally out

all it took was some elbow grease. and stuff.

First of all I would like to welcome you to G35club and Nico but I have to ask how did you do that?

With some patience and smartly and slowly yanked it out !

I saw a solution to the stuck key issue on another on-line board, and I was able to use the info to extract my key from the intelligent key port. If you look inside the port (you'll need a flashlight), you can see two white tabs on either side of the key (you might have to wiggle the key a little from side-to-side to see both of the tabs). Using a small flat-bladed screwdriver push against one of the tabs while using needle nose pliers to gently pull on the key. My key was stuck with the serrated edge pointing toward the door so I assume that the tab on the left side (toward the door) was the one holding the key in place. I worked the screwdriver against the left side tab for about 15 seconds to get it pushed out of the way, and I was able to get the key out (working it against the right side tab did no good). You don't need to push hard on the screwdriver or pull hard on the key (use too much force and I assume something would break). The dealership told me that there was no way to extract the key without ruining the port and they wanted to charge me $350 to fix the problem.