So your system was running on a prior video card just fine. You swapped out the older video card for the new one. You connected all power connectors to the molex for the video card and the system boots, but in order to see Windows successfully booted your having to move the video cable to integrated video.
* Have you installed the driver for the new video card yet?
Additional information on make/model of computer or if custom build... the motherboard, cpu, ram etc could help as well so we know what this video card is stuffed into and paired with for hardware.
You might be running into a PCI Express issue where your PCI Express slot is too old for the video card. Most cards are backwards compatible, but i have run into some cards that are PCIE 3.0 that do not play well with PCIE 1.0, 1.1, and 2.0 and act just like you have for a problem. My older gaming system is stuck in this category with PCIE 2.0 cards only seem to work with it and higher end 3.0 cards show no video yet windows boots as I can connect to the integrated VGA port and see the system running.I'll send it to service somewhere. Thread solved. Period
Sorry an answer or solution to your problem wasnt faster to come to be. Withholding critical info and lack of details only leaves us guessing what your issue might be.