quite a common complaint/problem with the 1530 xps is that the graphics card overheats on the machine, do you ever get a little shock from the metal casing at all? firstly i would try taking the battery out, disconnecting the power lead and pressing and holding the power button for around ten seconds, sounds stupid but it disperses all built up static and residual energy in the system, after that plug back in and try and turn on the machine, it should hopefully the boot for you, i have had around 5 of these in the workshop this year alone all with that same complaint, it even happens on the 1330 which is pretty much identical just 13 inch screen,
let us know how you get on :)