I tried installing VLC Player yesterday, and I got the Requires installation of untrusted packages error. I searched for hours for a solution to this problem, and finally came upon a suggestion that said to change servers for downloading updates from. I did this, and it gave me a 404 error when I clicked on "Check" in the Update Manager. I tried switching my server back to the main one (and after that, several other ones), but I am now still getting a 404 error:

And the other error I get when downloading or updating:

Edit:
Output of cat /etc/apt/sources.list:

deb-src http://us.archive.ubuntu.com/ubuntu/ precise main restricted #Added by software-properties



# See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to

# newer versions of the distribution.

deb http://us.archive.ubuntu.com/ubuntu/ precise main restricted multiverse

deb-src http://us.archive.ubuntu.com/ubuntu/ precise multiverse universe #Added by software-properties



## Major bug fix updates produced after the final release of the

## distribution.

deb http://us.archive.ubuntu.com/ubuntu/ precise-updates main restricted multiverse

deb-src http://us.archive.ubuntu.com/ubuntu/ precise-updates restricted main multiverse universe #Added by software-properties



## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu

## team. Also, please note that software in universe WILL NOT receive any

## review or updates from the Ubuntu security team.

deb http://us.archive.ubuntu.com/ubuntu/ precise universe

deb http://us.archive.ubuntu.com/ubuntu/ precise-updates universe



## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu 

## team, and may not be under a free licence. Please satisfy yourself as to 

## your rights to use the software. Also, please note that software in 

## multiverse WILL NOT receive any review or updates from the Ubuntu

## security team.



## N.B. software from this repository may not have been tested as

## extensively as that contained in the main release, although it includes

## newer versions of some applications which may provide useful features.

## Also, please note that software in backports WILL NOT receive any review

## or updates from the Ubuntu security team.

deb http://us.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse

deb-src http://us.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse #Added by software-properties



deb http://us.archive.ubuntu.com/ubuntu/ precise-security main restricted multiverse

deb-src http://us.archive.ubuntu.com/ubuntu/ precise-security restricted main multiverse universe #Added by software-properties

deb http://us.archive.ubuntu.com/ubuntu/ precise-security universe



## Uncomment the following two lines to add software from Canonical's

## 'partner' repository.

## This software is not part of Ubuntu, but is offered by Canonical and the

## respective vendors as a service to Ubuntu users.

deb http://archive.canonical.com/ubuntu precise partner

deb-src http://archive.canonical.com/ubuntu precise partner



## This software is not part of Ubuntu, but is offered by third-party

## developers who want to ship their latest software.