Someone may find this useful in diagnosing their HP or Compaq laptop boot failures that generally just show a black screen.

Source:  http://h10010.www1.hp.com/ewfrf/wc/document?lc=en&dlc=en&cc=us&docname=c01732674&product=1132551#N399

Caps Lock/Num Lock LEDComponent TestedError Condition
LEDs blink 1 timeCPUCPU not functional
LEDs blink 2 timesBIOSBIOS corruption failure
LEDs blink 3 timesMemoryModule error not functional
LEDs blink 4 timesGraphicsGraphics controller not functional
LEDs blink 5 timesSystem boardGeneral system board failure
LEDs blink 6 timesBIOSBIOS authentication failure