Thats driver in the second picture looks just like an AixiZ driver such as:
2pcs adjustable current laser diode driver 80-500mA w/TTL, AixiZ
Take a look at the picture in the link and you will notice that on the power input side where you have your red wire from the batteries there's also a pad on the opposite side of it that is called TTL+ and that also has to make contact with the power input red wire or that driver will not work. From what I can tell it doesn't look like it is. Can't tell you how many people have not realized this and thought their driver wasn't working. Same thing happened to me the first time I used one of those drivers. I've probably built at least 20 lasers since with those. Cheapest as far as I know to buy a pair of them right from AixiZ at the link I sent or from ebay through them.
A little secret that I've shared a couple times concerning those drivers is if you adjust the pot to max output you can turn it through the stop just a bit more before it goes to 0 (switches off) and run it unregulated as in the more voltage it gets the more output you get. Comes in handy if you want to push an LPC-826 diode to just over 400mW with a couple of fully charged 3.2V cells. Don't try 3.7V cells though or the diode will poof.
Anyways, what I do to connect both the TTL+ and the V+ is use my Dremel to make a little notch/cut from the end through both pads and then solder the wire to both sides.
If I remember correctly that driver will increase by turning the pot clockwise. I use a ceramic screwdriver if I adjust with power applied to help prevent a short.
I would also highly suggest that when you solder the wires on that you first tin both the wire and the pad and cut the wire back so that you don't have almost any extra soldered wire sticking out from the board. All you need is the bare tinned wire just long enough to solder it on.
I realize you are learning and that's great so don't take any criticism hard
I'm guessing the wires are long just for testing.
I tried looking for those batteries and the ones I came up with are not rechargeable. Are those rechargeable? What voltage does each one read? DON'T try and recharge a non-rechargeable battery. What size are those? Sure looks like this one I saw that's only 1/2 AA:
http://laserpointerforums.com/attachments/f38/49953d1453319030-more-problems-bdr-209-20160120_142637.jpg
If that's the battery it may not have the capacity to handle this.
What is your general location? I don't see even what country you are from...