If you have Ubuntu 11.10 it comes with Unity desktop gui, if you want to try
Gnome 3, you'll find it with Synaptic in the Meta Packages. As for using Apt-Get
in the Terminal, I'll let others point the way.

But it doesn't let me download anything on the Software Center or
through the Terminal.

Are you trying it wired or wireless? Were you able to download and install the
updates?

Wireless and no updates from last I checked.

There are update and bug fixes from Canonical almost daily except perhaps
on weekends and major holidays. If you have had your system running for
more than a few days without any updates then something is not working as
it should.

You connect wirelessly, which normally can do the job. Is plugging in a
network cable an option? I would certainly try that if possible. Is the
Wifi hotspot your own router? If it is not you may have encountered a setup
that doesn't allow downloading data - unusual but possible.

The whole thing is strange because I can surf the web without any
issues but when it comes to downloading updated or from the Software
Center it errors out saying check for an internet connection.

Open a terminal window and type the following...

sudo apt-get update

... we already know it will fail but the *exact* output from that
command will be useful in tracking down the root cause. So copy paste
that output and post back with it.

NB - to copy text from terminal, highlight with mouse then Right Click
on selected text and click on 'Copy'.