15.10 Steam Installation Doesn't Work

I tried installing Steam on a new installation of Ubuntu alongside Windows 7. I forgot to adjust the size of the partition after the installation so I had a pretty low amount of disk space. In the middle of installing steam I got an error message that looks like this:

So then I took the time to adjust the disk space.

After that I tried to launch Steam again to try to finish the install. Once opened I got the same error almost instantly.

After clicking Okay I got this message:

So now I have even more problems. I did some looking around and tried to fix that problem with solutions that other people with previous versions of Ubuntu but I did not solve that problem.

When I click okay on that error, Steam starts to load like this:

However after about 10 seconds it stops and I get the first error and it starts this loop over again.

At this point, I'm not trying to "Fix" this problem but I'd like to simply, entirely remove Steam and start over but I can't.

Any help would be much appreciated! Thanks!

EDIT This is my out-put when I run 'steam':

Running Steam on ubuntu 15.10 64-bit
STEAM_RUNTIME is enabled automatically
Runtime checksum: e0d069bbcb111e8ce740f52993b5dfcf  steam-runtime.tar.xz, expected ff08f6ce5972fe92d9764a8abed66f64  steam-runtime.tar.xz
Unpack runtime failed, error code 2
Error: Couldn't set up the Steam Runtime. Are you running low on disk space?
Continuing...
Error: You are missing the following 32-bit libraries, and Steam may not run:
libXtst.so.6
libXrandr.so.2
libgobject-2.0.so.0
libglib-2.0.so.0
libgtk-x11-2.0.so.0
libpulse.so.0
libgdk_pixbuf-2.0.so.0
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
Installing breakpad exception handler for appid(steam)/version(1449778863)
[2015-12-13 23:35:16] Startup - updater built Dec 10 2015 11:38:07
[2015-12-13 23:35:16] uninstalled manifest found in /home/max/.local/share/Steam/package/steam_client_ubuntu12 (1).
[2015-12-13 23:35:16] Found pending update
[2015-12-13 23:35:16] Installing update...
[2015-12-13 23:35:16] Extracting package...
[2015-12-13 23:35:25] Installing update...
[2015-12-13 23:35:25] Cleaning up...
[2015-12-13 23:35:25] Update complete, launching Steam...
[2015-12-13 23:35:25] Shutdown
Restarting Steam by request...
Running Steam on ubuntu 15.10 64-bit
STEAM_RUNTIME has been set by the user to: /home/max/.local/share/Steam/ubuntu12_32/steam-runtime
Runtime checksum: e0d069bbcb111e8ce740f52993b5dfcf  steam-runtime.tar.xz, expected ff08f6ce5972fe92d9764a8abed66f64  steam-runtime.tar.xz
Unpack runtime failed, error code 2
Error: Couldn't set up the Steam Runtime. Are you running low on disk space?
Continuing...

Running 'df -h' gives me this:

Filesystem      Size  Used Avail Use% Mounted on
udev            2.9G     0  2.9G   0% /dev
tmpfs           588M  8.7M  579M   2% /run
/dev/sda5       250G  7.0G  230G   3% /
tmpfs           2.9G  1.1M  2.9G   1% /dev/shm
tmpfs           5.0M  4.0K  5.0M   1% /run/lock
tmpfs           2.9G     0  2.9G   0% /sys/fs/cgroup
cgmfs           100K     0  100K   0% /run/cgmanager/fs
tmpfs           588M   64K  588M   1% /run/user/1000
/dev/sda1       673G  397G  276G  60% /media/max/Windows 7

Your steam-runtime.tar.xz file is damaged or corrupt.

Try running this command to delete it:

rm ~/.steam/ubuntu12_32/steam-runtime.tar.xz*

then run

steam --reset

First off, I just wanted to say thanks to everyone that pitched in! I had to use a combination of a few different answers to make it work.

First I had to figure out a way to completely remove Steam. Thanks to @Grammargeek. You need to run these commands:

sudo apt-get purge steam
rm -r ~/.local/share/steam
rm -r ~/.steampath
rm -r ~/.steam
rm -r ~/.steampid
rm -r ~/Desktop/steam.desktop

Once that has been finished I followed the install step provided by @Michael:

sudo apt-get install steam:i386

Finally (before I started Steam), I ran the "Steam Reset" command provided by @Neil:

steam --reset

Thanks for the help everyone!

Try removing steam by running this in Terminal (This can be opened by pressing CTRL+T):

sudo apt-get purge steam
rm -r ~/.local/share/steam
rm -r ~/.steampath
rm -r ~/.steam
rm -r ~/.steampid
rm -r ~/Desktop/steam.desktop

Then, free up some disk space. Finally, reinstall steam with:

sudo apt-get install steam