Try not to write too much on one line. So instead of
ScoreCounter.Text = Convert.ToString(Convert.ToInt32(ScoreCounter.Text) + 10);
try something like:
int currentScore = Convert.ToInt32(ScoreCounter.Text);
int newScore = currentScore + 10;
string newScoreText = Convert.ToString(newScore);
ScoreCounter.Text = newScoreText;
Set a break point (F9) at the start of the calculation, hit F5 to start debugging then single step (F10/F11) line by line once your breakpoint hit. Check the values are as you expect for each line.
Once you have a specific line not having the affect you expect, then you can google that - and if still having questions ask here.
It is much easier to get help if you can say "I have line X, I expect it to do Y, but I observe Z". As it is now, we can't see what you expect the code to be doing, and that makes it hard to help you.
PS: Great you name your text box ScoreCounter - it is nice not seeing TextBox1 as we normally see from beginners!