Bought a dell inspiron 5100. In order to get power to screen, so that it illuminates, I have to apply pressure to to top of lid when laptop is open. What is going on?

When you apply pressure to to top of lid when laptop is open -- you complete

A circuit that would otherwise be open -- commonly called intermittent circuit

As for a repair I really can not suggest the correct repair

Hope someone else can do better -- Good Luck

If it's still waranty, get it fixed asap so there is log or report somewhere that the unit has been in repair before