Disturbia (a remake of Rear Window) had the same problem -- how to keep a character who has access to all sorts of technology from calling the cops?
SPOILERS BELOW
The movie used several tactics:
1) The protagonist was under house arrest, so he couldn't flee very far.
2) He was under suspicion for being under house arrest, so the police didn't trust him.
3) The reason he was under house arrest is because he punched the brother of one of the cops assigned to his house arrest.
In short, the plot hedged the character in through a combination of technology restrictions and social pressure. Once one of those rules are broken -- when the character decides to flagrantly violate his house arrest -- the film shifts gears quickly to a slasher flick.