Thankyou @Jim M, I've found an old third party app that was causing the blank screen. I don't know what to do now because it is an app we use as main management for our community, but at least I know where the problem cames from...
@Washerhelp thankyou but I already know you need to type the right PHP path into your cron task from your hosting management panel. My problem did not come from there. But regarding what you say, when you check "cron task" in the community settings it tells you what you need to type, including the path, you only need to make a "copy paste" and job's done ! 😉
And beware for the others, the PHP path is not always the same, it depends on your hosting installation, you need to refer to the ACP path to type the right one !
Thankyou all for your advices, now at least I know where my problems came from.