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Computer comprimised. Cannot access update manager cannot remove files HELP?

I have not done much of anything because I dont know what to do.Im running peppermint 3 and one day i came home to a non responsive computer. cannot update files change or manage anything.

Peppermint 3, cannot run update manager. strange happenins

My computer is not responding. I cannot run update manager or any type of files. I do not know how to take control back. Someone please help.

Code:

GPG error: http://us.archive.ubuntu.com precise 

Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <ftpmaster@ubuntu.com>

GPG error: http://ppa.launchpad.net precise 

Release: The following signatures were invalid: BADSIG 5A9BF3BB4E5E17B5 Launchpad PPA for chromium-daily

GPG error: http://ppa.launchpad.net precise 

Release: The following signatures were invalid: BADSIG B725097B3ACC3965 Launchpad lffl

Failed to fetch gzip:/var/lib/apt/lists/partial/us.archive.ubuntu.com_ubuntu_dists_precise_main_source_Sources  

Encountered a section with no Package: header

Failed to fetch gzip:/var/lib/apt/lists/partial/us.archive.ubuntu.com_ubuntu_dists_precise_multiverse_binary-i386_Packages  

Encountered a section with no Package: header

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



u_dists_precise_universe_binary-i386_Packages, E:The package lists or status file could not be parsed or opened.

This comes up in terminal. I am getting no where.

ERROR###ERROR###ERROR###ERROR###ERROR###ERROR###ERROR
E:Encountered a section with no Package: header, E:Problem with MergeList /var/lib/apt/lists/us.archive.ubuntu.com_ubuntu_u_dists_precise_universe_binary-i386_Packages, E:The package lists or status file could not be parsed or opened.

this is what i get

I am very new to this whole terminal thing and I am not having any luck running anything im finding on this site. If someone wouldnt mind pointing me in the right direction that would be great.

What command gave you that error? Please post the exact command and the exact error message. And please be more specific. What do you mean "unresponsive"? Does it boot? Can you login? Do applications launch? As I understand this is a web-o-centric distro, so is your network connection working?

I get that error when I try to open synaptic package manager. I can boot but my Firefox will not load. I cannot run update manager. Connects fine. Cant understand why it would just stop performing.

I am assuming you have graphical login and a network connection:

From a terminal;
sudo apt-get update

And then;
sudo apt-get upgrade

Report what happens...

There may be more to do once you respond.