When I got my used PS4 from friend and the controller we reset it all and the controller and system were both fully functional, and I went to go sync or connect it and it flash blue once or twice then shut off, I watched a ton of YouTube videos and none had the same problem, what do I do?
Is this a Sony brand controller or a third-party controller?
First party controllers usually only have issue if disconnected for a very long time or if the controller was formerly connected to a different PS4.
Are you positive the controller is charged?
If the controller doesn't have enough charge, it will flash blue and and appear to go dead before attempting to connect. The power cycle for a controller is to first check total charge and then attempt a connection. No charge, no connection - pretty basic.
Barring the above:
As the first person who took their time to graciously answer you, first connect the controller to the PS4 with the USB cable to register the controller and PS4 together. This allows the PS4 to retrieves the BT address of the controller. If the light turns orange on the controller, it is charging but you can operate hte PS4 with it plugged in and you now know that the controller works when connected, at least.
Then test the controls by navigating the menu system and finally by holding the PS button on the controller to turn the power off the PS4.
Finally, turn the power to the PS4 "on" by pressing the PS button on the controller - disconnect the cable and attempt to power it on with the PS button on the controller.
If it powers up, you're good (probably still want to let it charge). If not, you know it needs to charge and then let it do so and try these steps again.