Beginners code, loop doesn't detect unplugged pin
SInce I can coment I have to write this as answer.
there are two ways of understanding your question:
If you dont want it to ever blink again then simply remove
ledBlinked = false;
If you are trying to prevent the blinking until the button is depressed and pressed again then first think I see is the error in blinkLed function as
for (int i=0; i&lt;=times; i++) would run times+one time. because it runs first with value of i being 0 (Eg times=4 would run for i equal 0,1,2,3,4 -&gt; Five times ) So correction to for (int i=0; i&lt;times; i++) would run correct number of times (Eg times=4 would run for i equal 0,1,2,3 -&gt; four times )
Although as you are not checking status during the running of blinkLed function for the status of the button, if you release it while blink is running the script would not notice unless its still unpressed when script gets back to Loop.

Although since hardware operation take more work then logical operation I would recommend if...else statement rather then multiple hardware operations. Although they make code simpler to read
if(digitalRead(10) == LOW){
         if(ledBlinked != true)...
   } else { ...}