What caused the improper shutdown? More importantly, what was happening when that happened? What was running, and what were you doing?
Ok, so now to answer your question:
When you get to the prompt mentioned above, try to see what's mounted and how it's mounted, to do this type:
It should show you what's mounted, and what options it was mounted with. What you need to look for is to see if your / filesystem is mounted read-only. If it is (we hope) then you can safely run your fsck (read Scan Disk) on the disk. So, now you need to know what device to check. To find which device it is, you can either look at mount again and see what device / is mounted on; OR you can use fdisk to display your devices:
/sbin/fdisk -l (/SBIN/FDISK -L lowercase)
And then run fsck on that device similar to:
fsck -p /dev/hda1
Where /dev/hda1 is the device it actually is.
Be careful, and good luck!