Safari can be locked in System Settings - Restrictions. Check to make sure that Safari is enabled. There is not a direct connection between the action of password change and restrictions getting enabled, but it is something that needs to be verified. Also the iPad has a little bit of an issue on occasions after the rare app crash that it does not open right again afterwards. Double tap the one button and close all apps listed. Then try it again. If that does not work, I would power cycle and then try it. If that does not work then try and reboot by holding the one button and the power button for many seconds. If that doesn't work, your only thing else to try is to factory reset or restore to a previous backup when it did work.
Answers & Comments
Safari can be locked in System Settings - Restrictions. Check to make sure that Safari is enabled. There is not a direct connection between the action of password change and restrictions getting enabled, but it is something that needs to be verified. Also the iPad has a little bit of an issue on occasions after the rare app crash that it does not open right again afterwards. Double tap the one button and close all apps listed. Then try it again. If that does not work, I would power cycle and then try it. If that does not work then try and reboot by holding the one button and the power button for many seconds. If that doesn't work, your only thing else to try is to factory reset or restore to a previous backup when it did work.