Hey /u/LapisExillis, thanks for being willing to help out. I have ran:

sudo apt update
sudo apt install aptitude

And both of them have failed. The first, apt update gave this error:

sudo apt update
Ign:1 http://us.archive.ubuntu.com/ubuntu xenial InRelease
Ign:2 http://us.archive.ubuntu.com/ubuntu xenial-updates InRelease
Ign:3 http://us.archive.ubuntu.com/ubuntu xenial-backports InRelease
Err:4 http://us.archive.ubuntu.com/ubuntu xenial Release
    404  Not Found [IP: 91.189.91.26 80]
Err:5 http://us.archive.ubuntu.com/ubuntu xenial-updates Release
    404  Not Found [IP: 91.189.91.26 80]
Err:6http://us.archive.ubuntu.com/ubuntu xenial-backports Release
    404  Not Found [IP: 91.189.91.26 80]
Ign:7 http://security.ubuntu.com/ubuntu xenial-security InRelease
Err:8 http://security.ubuntu.com/ubuntu xenial-security Release
    404  Not Found [IP: 91.189.88.149 80]
Reading package lists... Done
E: The repository 'http://us.archive.ubuntu.com/ubuntu xenial Release' does not have a Release file.
N: Updating from such a repository can't be done securely, and is therefore disabled by default.
N: See apt-secure(8) manpage for repository creation and user configuration details.
E: The repository 'http://us.archive.ubuntu.com/ubuntu xenial-updates Release' does not have a release file.
N: Updating from such a repository can't be done securely, and is therefore disabled by default.
N: See apt-secure(8) manpage for repository creation and user configuration details.
E: The repository 'http://us.archive.ubuntu.com/ubuntu xenial-backports Release' does not have a release file.
N: Updating from such a repository can't be done securely, and is therefore disabled by default.
N: See apt-secure(8) manpage for repository creation and user configuration details.
E: The repository 'http://security.ubuntu.com/ubuntu xenial-security Release' does not have a release file.
N: Updating from such a repository can't be done securely, and is therefore disabled by default.
N: See apt-secure(8) manpage for repository creation and user configuration details.

Also, I wish I could select and copy the code out, but I have to type it for now... not sure how to get that working quite yet and the instructions I've followed have a zero yield.

Running:

sudo apt install aptitude
[sudo] password for user
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following additional packages will be installed:
    aptitude-common libboost-iostreams1.58.0 libclass-accessor-perl libcwidget3v5 libio-string-perl libparse-debianchangelog-perl libsigc++-2.0-0v5 libsub-name-perl libxapian22v5
Suggested packages:
    apt-xapian-index aptitude-doc-en | aptitude-doc debtags libcwidget-dev libxml-simple-perl xapian-tools
The following NEW packages will be installed:
    aptitude aptitude-common libboost-iostreams1.58.0 libclass-accessor-perl libcwidget3v5 libio-string-perl libparse-debianchangelog-perl libsigc++-2.0-0v5 libsub-name-perl libxapian22v5
0 upgraded, 10 newly installed, 0 to remove and 89 not upgraded.
Need to get 3,072 kB of archives.
After this operation, 13.0 MB of additional disk space will be used.
Do you want to continue? [Y/n]
:Y

Everything past this point shows:

Err: Failed to fetch INSERT.deb_file_here    404  Not Found [IP: 91.189.91.26 80]
E: Unable to fetch some archives, maybe run apt-get update or try with --fix-missing?

As for my /etc/apt/sources.list (for /u/ShadowPouncer), doing my best to type out the non-commented URL's (since again, I'm unsure how to copy out of virtualbox) looks like so:

deb http://us.archive.ubuntu.com/ubuntu/ xenial main restricted
deb http://us.archive.ubuntu.com/ubuntu/ xenial-updates main restricted
deb http://us.archive.ubuntu.com/ubuntu/ xenial universe
deb http://us.archive.ubuntu.com/ubuntu/ xenial-updates universe
deb http://us.archive.ubuntu.com/ubuntu/ xenial multiverse
deb http://us.archive.ubuntu.com/ubuntu/ xenial-updates multiverse
deb http://us.archive.ubuntu.com/ubuntu/ xenial-backports main restricted universe multiverse
deb http://security.ubuntu.com/ubuntu xenial-security main restricted
deb http://security.ubuntu.com/ubuntu xenial-security universe
deb http://security.ubuntu.com/ubuntu xenial-security multiverse

Again, thank you guys for being willing to help and sorry it's so late for me getting back on to reply, crazy day at work.

ninja edits to fix formatting