cant start my iphone 6 when upgraded to 9.3.4

Press the Sleep/Wake and Home buttons and hold them for at least 10 seconds.

If this does not help, take a look these Apple Support articles:

If your iPhone, iPad, or iPod touch doesn't respond or doesn't turn on - Apple Support

Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support.

As a final step, try the recovery mode. Turn your device off, then plug it to your computer with the home button pressed. Keep the Home button pressed until you see the iTunes logo on the screen of your iPhone. After that on your computer you should see the iTunes window saying your iPhone needs to be restored to factory settings. Click on the restore button.

More info here: https://support.apple.com/en-us/HT201263

If these steps don't work, contact Apple and ask for help.

https://www.apple.com/support/iphone/contact/