Umount

OK, sorry to keep you waiting, but this seems to be a very hard problem. As my own setups looks nearly equal i only could imagine three possibilites:

1) For some reason your "umount" isn't on /dev/hda7, so after being umounted it wouldn't be possible to umount /dev/hda7.

Validation: "locate umount" and check the directory. Be sure your Database is up to date.
Solution: As umount should be static, just copy it to /bin or another surely on /dev/hda7 located directory

2) For some reason umount isn't build static, and some of the libraries are on another previous unmounted partition.

Validation: "file umount" says if umount is dynamic or static. With "ldd /bin/umount" (or whatever path it is, ldd needs the full puth) you can see what libraries are needet, so it could be tested if they are located on another partition.
Solution: like 1), just copy the libraries to a directory located on /dev/hda7 or build a static umount.

3) There is something relay rotten on your harddisk. Probably it would help to switch into singleusermode and do a "e2fsck -c", and thereafter a "e2fsck -p", the first to do a badblock-check, the second to check and automatical repair.

I hope, some of this could help you. Please report if not or you find any other reason.