Can cyclone III comes into the user mode if AP config failed?

I'm not aware of the term "POR error" used anywhere in the Altera documentaion, nor can I read a reasonable meaning into it. What do you mean?

If you're referring to a state where POR isn't released, check all power supplies that are monitored by the POR circuit as well as the device soldering, as already suggested by Daixiwen. nCONF held permanently low (with proper pull-up) suggests in fact active POR, also inaccessible JTAG.