If I do set_time_limit(50) or ini_set(\'max_execution_time\',50), then when I echo ini_get(\'max_execution_time\') on my localhost i g
Does GoDaddy allow you to edit their remote PHP.INI file, or (achieving the same function) set those options at runtime? Many restrictive hosts (and I don't know this about GoDaddy one way or the other) won't let you futz with PHP options either via the config file or at runtime as you did on WAMP. It could be that though you're still calling that function, it's not being applied.
Use
echo 'Time Limit = ' . ini_get('max_execution_time') .
The manual says that if it's set at all in the PHP.INI, that will override this runtime. PHP Manual on set_time_limit