Last night my sister was on the computer and she shut it down by just pressing the power button.I heard it was never good to shutdown a unix system from the power button(I always do the shutdown -h now), how do I know if the filesystem has been damaged or something like that?

if a filesystem is damage, an error would be displayed at boot up or filesystem would be umountable.

fsck (filesystem check) would report an inconsistance filesystem at boot up, if is configure in /etc/vfstab, if not you can run
fsck on filesystem

the syntax is on solaris

fsck /dev/dsk/c#t#d#s#

or run fsck on mount point

eg
fsck /
fsck /usr

My problem is

first, the filesystem could not be mountable, and ask to go into filesystem maintenance. Then after typing the password, at the # prompt, I did "halt", then it said: syncing file system ... done
program terminated
OK
OK

Anything I entered, it returns OK, just lik
OK
OK

Then seems I could not do anything, including the shutdown buttom.

So what should I do?
Thanks for helping

You really should have started your own thread for this, but anyway..

At the ok prompt, type the command 'boot'
When it asks for the password give the root password.

then enter

fsck -y

Ok, thanks.

Most propritary boxes (SUN IBM HP SGI) issue a controled shutdown when you press the power off button, so they dont just kill the power.