That looks like (and should be based on the system model number) a blue laser by RGB in hungary. Its likely to be 473nm DPSS rather than 44xnm from diodes.
Dont concern yourself with the current draw from the mod input - its a control input that will show only negligable current draw - that said if it pulls an amp or 2 then you may have a prob

What would be of greater use is to vary the mod input and observe the 5V power supply current consmuption. There will be a significant (maybe an amp) draw on this with zero volts on the mod input, as the diode will likely be biased so that it will be just below threshold at zero input. The current should increase in a reasonably linear fashion as you increase the mod input volts. The current of 4.5A may seem alot but there will be a multiwatt 808 pump diode in there so I doubt thats a crazy figure. I am concerned however that the volts are dropping to 3.2V - can your PSU supply enough current? - i would hope it can and am not trying to insult you - just important to know!
One thing you can do is use a ccd camera (webcam mobile phone) to look for ir. Place a white card a few inches from the output and look at the card through the camera. If you see a pink/purple glow then there is ir being emitted. If its really bright then the head may well be working but the SHG may not be functional. If you see no glow on the card try pointing the camera directly into the laser output window. This may seem daft but if there is enough ir coming out to damge the camera you would see the glow on the card. Doing this you may see some ir glow inside, if you do and its faint then the diode may well have gone to diode heaven.
As you rightly pointed out the head should get some warmth as the TECs do their job but if its getting very hot very quickly this could be a problem and explain why there is no blue output as Blue DPSS need pretty close control of temperature to work.
Hope it helps - keep us informed and keep asking questions.
Rob
PS look on the edge of the driver card - it says RGB LAser Systems
