Hello [MENTION=111848]saikiasunny[/MENTION]
I have read your camera issue and it seems weird but not uncommon. Lot of Nikon and Canon DSLR users have faced this problem but its mostly hardware related and could only be fixed by service center or replaced.
I have D3200 and I have checked all the settings but none (except IR release mode) could stop shutter button from taking photos when focus is green. After-all, our cameras are basic DSLRs so there aren't many options and when we choose factory reset, the camera should function normally, if not its hardware issue.
Popup flash is TTL type, that means the camera fires flash two times (Before shutter is released and while shutter is open). I think your camera couldn't fire the pre-flash hence its not taking photos.
Problem could be from minor connection issues (like nac shown a video to fix) to major capacitor or other internal component. It would be connection problem when camera cannot detect popup flash when opened but in your case, camera detects the flash so it seems to be internal component(s) fault.
TTL external flash has full connection to camera and when attached popup flash doesn't open but due to flash problem in your camera, I doubt external flash gonna work either. Manual external flash has single connection to camera and it has to work but you have to guess the exposure yourself.
I advice you to take the camera to Nikon service center and get the problem resolved asap. If it has bad capacitor and if leaks then more issues may raise.
Thanks...
Best Regards