Hi @luuktoo ,
Sounds like a loose connection somewhere, as simply moving it should not cause what appears to be a power failure. (By “''screen goes to stripes en turns off”'' I assume you mean that the laptop turns off and not just the screen).
Does it do this when you have the charger connected and switched on?
If not, check the connection to the battery to ensure that it is secure.
You probably don’t need this but here’s a link to the [https://topics-cdn.dell.com/pdf/latitude-e5440-laptop_owners-manual_en-us.pdf|service manual] for your laptop.
Pressing the case is a different matter as you may be causing something to move, perhaps by distorting it and again causing a power disruption. If it is loose it would take much movement.
Can you isolate the spot ''exactly'' where you have to press the case to make this happen? Is it the same spot every time?
If so you may be able to see what is below the spot on the case that you’re pressing and see if anything is amiss.