How do I connect these video cables?

I'm installing some new security cameras where our old ones were. One is on a brick wall, with wires being run through where they drilled through the brick/grout. The previous installation had the cables exposed, but the new camera is built to hide them in the wall, so I needed to push the cable back into the wall.

However, it looks like the original installer ran plain cable through the hole they drilled in the brick, then attached a BNC connector to the end. This makes the hole too small to get the connector back through. I couldn't widen the hole with the cable still in it, of course, so I cut the connectors off the end of it and the new camera and fished it up through so I could connect them inside.

Here's where I'm confused: the original cable is coax (used with bnc connector). The new cable on the camera (also with bnc connector on the end) just has a small blue wire and small yellow wire inside. Which wire goes to which part of the coax, if I'm splicing them together? I tried both ways (yellow to braided, blue to internal, and vice versa) and neither worked (I'm running all new wire now but had to stop for the day), but I am afraid trying it the wrong way may have fried something? I'm no expert but get by with YouTube’s help most of the time, but I haven't seen anything that will explain this.