Flashing caps lock (older systems) is usually a memory problem.  While proceeding with the good instructions provided in the other reply, also remove and replace the memory modules while you have the battery out and the power disconnected.  That may solve the issue.  If it doesn't, and you have two modules, try one module at a time in each slot.  If one module halts POST in both slots, it's bad -- replace it.  If both modules halt POST in one slot, the slot is bad, making the system a candidate for replacement;  it won't be worth replacing a mainboard in a system this old.  
My Dell Studio XPS 1645 laptop is not displaying anything on the main screen or 2nd screen and is also flashing the caps lock and all the volume lights. Also,  the keys are lit up while the PC is obviously not booting to Windows because of the simple fact that the computer immediately turns off the second I press the power button. Does anyone have any ideas what could be happening?
No screen, no boot.