HP Pavilion dv6z 300 LEDs and fan turn on, display is completely black

Try running it with different or a single RAM module. This often works to determine if one (or both) RAM modules are bad. The blinking caps lock light usually means the RAM or motherboard has failed on an HP laptop. Both are plausible, especially if yours includes a dedicated GPU.

If you continue having problems, the next thing I’d recommend is cleaning the RAM module pins and blowing out any dust in the slots with canned air. If this doesn’t work, purchase some a matched RAM set; RAM should not be mixed and matched if you can avoid it. If this works, throw the original RAM out. Do not keep it around as it has an intermittent failure.

If the RAM doesn't fix it, the GPU is bad. It isn’t worth trying to repair this since the only way to permanently fix it is a new motherboard that has never been reflowed or a GPU replacement done at a shop that does BGA rework. On top of that, many HP laptops are known to kill the GPU’s due to excessive heat since they don’t know how to cool a dedicated GPU correctly (On top of that, they are known to sell defective laptops with known problems). This happened with the 2007 DV Series; it took a lawsuit for them to fix it and make things right and they still found a way to screw owners of these bad laptops over; they only covered one GPU for free, even though both are known to fail.