Something clearly isn't right so you'll need to troubleshoot it. The fact that the pixels are glowing white indicates that they're getting power.
Possibility: The controller isn't outputting the correct data for any more pixels than the first working strand. How to check this: Swap the non-working pixels into the place of the working ones.
Possibility: The first pixel in the non-working strand or the last pixel in the working strand is faulty. How to check this: The above check would work.
Possibility: A connector is faulty and not passing on the data to the strand that doesn't work. How to check this: Try the above check and if that doesn't work, examine or change the connector at the input of the non-working strand.
Possibility: You've connected the wrong end of the non-working strand to the data from the working strand. How to check this: You might be able to see the labels for DI and DO (data in and data out) depending on the type of pixel. Otherwise just try connecting the other end of the strand of pixels to the data.
Possibility: Some pixels glow when their input voltage is too high. How to check this: Measure the voltage that they're getting.
Possibility if using multiple power supplies: You've accidentally connected the positive outputs of the power supplies together, probably through the lights. I think this is unlikely when considering the behaviour of the pixels but it is a good idea to rule it out whenever anything misbehaves. How to check this: Check your wiring and cut the positive line in the strands of pixels half way between each power supply.
Possibility (already mentioned by notenoughlights): The pixels use a slightly different signal and they can't understand each other. You can rule this out if they are the exact same type of pixel from the same order. How to check this: Connect some pixels that exactly match the working strand to the end of the working strand and see whether they light up. Connect the non-working strand directly to the controller's data output. You still need to check that it isn't faulty.
Possibility: The data wire between the two strands of pixels is too long and the signal can't travel that distance. How to check this: Try a shorter wire between the two strands of pixels. If this fixes the problem, you need to add null pixels or a pixel extender.