>ドアが閉しまります！ wrong
ドアが閉まります! correct
"ドアが閉まります： DOA GA SHIMARI-MASU;The door will close"
You might think this translation is strange in use of "close" but door close by itself in Japan.
In this case, "GA" simply indicates the subject of the sentence.
"ドアは閉まります
OA WA SHIMARI-MASU; as for the door, it is gong to close(or to be closed)." sound strange because "WA" implies some comparison. Whe you say "MIGI NO DOA WA SHIMARI MASU:The right side door will be closed" will make sense.
>ga is used to introduce something new.
I cannot accept this definition. Do you have any example?