'10 GLK350 key fob does not lock
 

After many attempts it might work. No problem with unlock.

I only have one key. What is it likely to be?

Does the LED in the key blink when you press the lock button? Does your spare key work? Have you tried putting in fresh batteries......???

what happend to the other key? go to dealer order another key if you have the same problem it is with car if it works then problem is with key.
you should always have at least two keys for theses newer cars in case one stops working you can still use the car while the dealer orders a new key. when lost or broken you can not just walk into the dealer and have them sell you a new key they will have to order it and you will have to return to pick it up some dealers require the car be there when you pick up new key to varify it works correctly so if you have no key you will have to tow car down there

your problem is probably the button on the key
push the lock button in car and see if it works both ways