That's a predicament you're in
I don't think there is a way to bypass the key card.
If the card isn't been detected it's a fault on the round black coil inside the key card, probably one or more of the three solder joints on it have cracked.
Give this a try....
https://www.youtube.com/watch?v=-hs1prW6Ct4If that doesn't work I would take my time and cut the card open, there are videos on you tube showing how to do this, study a few of them so you know what you are doing, make sure just to cut in a little bit don't put the blade in deep as you don't want to hit the circuit board.
With the card opened up you stand a much better chance of finding someone who could solder the coil contacts for you if you can't do it yourself.
Alternatively you could try and wedge the coil to make a contact and tape the card back together as a temporary measure.
You can buy new replacement card covers on ebay so it's not the end of the world if you mess yours up a little when cutting it open.
Hope you get it sorted.
Cheers.