LED, 2 way switch wiring not working
The original LEDs were driven by a constant-current source and were therefore wired in series.

Your replacement LEDs need to be driven by a constant voltage, and therefore need to be wired in parallel, which is how you bench-tested them.

You're going to have to figure out a way to repurpose the wires inside the wall in order to get the LEDs connected in parallel rather than in series. It may be necessary to pull new wires.




  I found out each hole in the hole has the 2 cables the old LEDs used AND 2 more cables, that were wrapped together. So now I have 4 cables. Each pair, has a positive and a negative. Any idea what I should do?


That's actually good news. It means that you don't need to pull any new wires.

What you likely have is "zip cord" running from hole to hole, wired something like this (original setup):







You just need to reconnect the wires in the holes like this: