Your diode seems to have nearly no output. My 10mW bluray will cause white printer paper to fluoresce a very bright blue where the spot hits it. You sound like you have a dim violet LED at best. Also, as mentioned a few times already, 6V is not enough for a bluray when you use a linear driver like the LM317. You need at least 9V, you can test off a 12V bench supply to rule out bad batteries. The bluray diode needs about 5.5V and the LM317 has a reference voltage of 1.25V, but needs a little more overhead. Two fully charged lithium cells totalling 8.4V is usually the minimum to run a PHR and linear regulator of the LM317 type, three lithium cells is better. When ordering laser diodes, it's best to get more than one. It's Murphy's Law ... if I only have one LD and need the laser badly, the LD will be dead already, or I will drop it and step on it or something like that. Get a new diode and go through all the steps. Bench power to regulator and test load, verify and set current, disconnect from power, short cap, solder LD (quickly, no overheating), if it's winter where you are, use antistatic precautions, test driver and LD off bench supply, if good, test off batteries, if good then assemble laser ...
Best of luck, you will succeed!