You're missing all your semicolons. ";"
The script is simply skipping straight to the end, I do believe.

This is my own, and it worked last I checked.

level_trigger_7 = [echo "text ere please sir";
sleep 5000
[echo "blahhhh";
sleep 2000
[echo "more blahh";
sleep 2000
[echo "text here";
sleep 1000
[ trigger 12 1]]]]]

Try this out, and make sure your door tags are correct, and make sure the door state is 11. ( it is 11, isn't it? )

alias level_trigger_1 [
echo "Glad to see you made it!";
sleep 3000 [
echo "All of your systems are functioning normally.";
sleep 3000 [
echo "I am going to open the stasis room door.";
sleep 3000 [
echo "Make your way down to the training room.";
sleep 3000 [
echo "There you will perform combat as well as basic training.";
sleep 3000 [
trigger 3 1]]]]]]

Line breaks imply semicolons for the parser. Therefore, semicolons are only required if you put more than one command on a single line. Having extra semicolons at the end of statements wont harm anything.
For example,
echo "say something"; sleep 2000 [ echo "hi" ]

Commands require everything to be on the same line. Example:
sleep 3000 [ echo "say something" ] //works
sleep 3000
[ echo "say something" ] //does not work

You can also have multiple lines as you have above
sleep 3000 [
echo "say something"
echo "say something else"
]

Now as to your original request, there is nothing syntactically wrong with what you have. The code is completely correct. However, the parser can sometimes do weird things and cause funky errors. This is usually caused by an incorrect grouping of commands that is grouped by the ['s and ]'s.

I usually go by the rule of having at least one space before and after every [ or ].
So the last line you gave I would change to:
trigger 3 1 ] ] ] ] ] ]

This should guarantee everything gets grouped correctly.

A different option you can try if none of these work would be to rewrite it and keep everything separate instead of nested and do some math and change the sleeps:

alias level_trigger_1 [
echo "Glad to see you made it!"
sleep 3000 [ echo "All of your systems are functioning normally." ]
sleep 6000 [ echo "I am going to open the stasis room door." ]
sleep 9000 [ echo "Make your way down to the training room." ]
sleep 12000 [ echo "There you will perform combat as well as basic training." ]
sleep 15000 [ trigger 3 1 ]
]

srbs