Both trigger but at different times in the process:
- max_input_time is the time that PHP takes to parse the request and provide its $_POST, $_FILE etc, structures.
- max_execution_time is the time that your script may run after the request is parsed.
So I'd suggest you do some kind of logging (to a file, not to the browser) in your PHP script to see if the script is actually executed. If it is not executed, then max_input_time has triggered, if it is executed, then your script probably took too long and max_execution_time has triggered.
note though, there may also be other factors leading to a blank page being delivered, so you should really check your php and apache logs for any errors.