Should be:

adding use strict; use warnings; to your code will help find such mistakes. The remainder of your problem is that if $char is not "a" then you break out of the while loop, at which point $position is still zero and not equal to the length of $string.

Consider basic debugging of your code, making use of http://learn.perl.org and the tutorials section.

There are easier ways of achieving your goal, however as a learning exercise I think you should at least figure out everything that's wrong with this approach.