LED Case Lighting Installation

Solution 1:

Red is +5V, yellow is +12V, black are both grounds (the one on the red side is for the 5V, the one on the yellow side is for the 12V but I'm pretty sure you can use both of them).

Here's the exact pinout, just for reference :

So if your LED strip uses 12V, then cut its power cable, insert the ground wire into one of the ground pins (the two at the center) of the male molex connector (coming from your PSU), and insert the positive wire into the +12V pin of the molex connector. You can use whatever you want for insulation, assuming both wires are held together they should stay in place and provide enough electrical contact to power the LEDs.

The second product you mentioned - the weird two female connectors molex cable is useless to you as you can't even connect it to your PSU. You maybe wanted to buy this cable instead which has a connector that can connect to your PSU. In this case, cut the black and yellow wires and solder them to your LED controller's power cable, like this :

And no crimp too needed, it depends on your level of perfectionism. You can use my dirty solution that I proposed above which just requires you to insert the wires into a connector and secure all of that with some duct tape, you can do better by using an actual molex connector and soldering the wires to it as proposed in my second solution, or if you really want to you can buy a molex connector and crimp it to the power wires of your LED strip, but that's way too overkill for such a simple mod.