Out of the blue I can't start nautilus today. When I try to open any directory it tries to open it, and sometimes I even can see the content of directory, but finally it's closed, after that there are no icons on desktop. When I tried to launch nautilus from terminal, I got:

$ nautilus .
Initializing nautilus-dropbox 0.7.1
Initializing nautilus-gdu extension 
Segmentation fault (core dumped)

I've tried to move ~/.local/share/gvfs-metadata folder, I don't have nautilus-open-terminal package and don't have file /usr/local/lib/libgtk-3.so.0

Also I can't update system right now. All the time I'm getting the the same hash-sum error:

$ sudo apt-get update
[sudo] password for dmitriy: 
Ign http://mirror.mirohost.net precise InRelease
Ign http://mirror.mirohost.net precise-updates InRelease                       
Ign http://mirror.mirohost.net precise-security InRelease                      
Hit http://mirror.mirohost.net precise Release.gpg                             
...
Ign http://ppa.launchpad.net precise/main Translation-en             
Hit http://mirror.mirohost.net precise-security/restricted Translation-en
Hit http://mirror.mirohost.net precise-security/universe Translation-en
Fetched 1 B in 1s (0 B/s)                               
W: Failed to fetch gzip:/var/lib/apt/lists/partial/mirror.mirohost.net_ubuntu_dists_precise_universe_source_Sources  Hash Sum mismatch

E: Some index files failed to download. They have been ignored, or old ones used instead.

Any ideas how to rescue my system?

UPD: In syslog I have the following errors:

Jul  7 21:35:02 dmitriy-desktop kernel: [   58.059141] nautilus[1991]: segfault at 7fc09d9bb700 ip 00007fc0abb5feb6 sp 00007fff6caa4cf8 error 4 in libc-2.15.so[7fc0aba24000+1b3000]
Jul  7 21:35:39 dmitriy-desktop kernel: [   94.356490] update-notifier[3358]: segfault at 7f6507611700 ip 00007f64cc221eb6 sp 00007fffbcc0dd88 error 4 in libc-2.15.so[7f64cc0e6000+1b3000]
Jul  7 21:37:45 dmitriy-desktop kernel: [  220.501859] nautilus[3629]: segfault at 7f9b9744c700 ip 00007f9b7c9c6eb6 sp 00007fff72e990f8 error 4 in libc-2.15.so[7f9b7c88b000+1b3000]

UPD2: Ubuntu version is 12.04.