tmadden: You can download the proprietary flash software here. It should install the repositories too from memory. Otherwise you can download Google Chrome (as opposed to Chromium which is the technology Google Chrome is built on) which has flash built into it.
Also from memory when you install Ubuntu it gives you the option to enable 3rd party proprietary software which is 'non-free', such as the fluendo mp3 codec and flash. It isn't the most obvious box in the world to tick but it can save some hassles later on.
tmadden: Interesting... I used to have problems with flash while using Firefox in previous versions of Ubuntu but installing Chrome always solved it. I found this while rummaging around the adobe site;
I can't view rich media content. How do I get Flash Player to turn on?
It's possible that you could have disabled Flash Player in Chrome. To reenable it:
Type ?about:plugins? (without the quotation marks) into the address bar at the top of a Chrome browser window.
Click ?Details? at the upper-right corner of the page.
Find the ?Flash? (or ?Shockwave Flash?) listing on the Plug-ins page and click the corresponding ?Enable? button.
Close all Chrome windows and restart the browser.
Although given you have a fresh install the plugin will probably already be enabled. Other than that maybe it's a hardware issue? Are you using proprietary graphics drivers or the open-source ones?
tmadden: Which version of Ubuntu are you running? It looks like you've opened jockey which is an old way of looking for additional drivers, it's now handled in the software sources application. I can't remember if it was dropped from the last release or the current one. Although to be honest it shouldn't really matter which version of Ubuntu you're running, if flash is installed it should still work.
The graphics card thing is a bit of a long shot too really, but might be worth looking at. Proprietary graphics/wifi/printer etc. drivers generally don't install automatically because of their 'non-free' nature, but Ubuntu and it's derivatives are pretty good at making it as easy as possible (although it wouldn't hurt them to make it easier again like it was with jockey, which would pop up not long after the first install pretty much do it all for you). Older nVidia cards only work with the nouveau (open-source) drivers as they're no longer supported by the manufacturer. Anything from the 6xxx series up should work with the proprietary drivers. I've never used ATI cards but from what I've heard/read they aren't very reliable in Linux due to the lack of interest by AMD, proprietary software is available for them though. Intel cards work too but I'm not sure which type of software they use. It could be that you need the proprietary software to get the rendering power out of your graphics card. If there are proprietary drivers available either jockey-gtk or Software Sources will let you know, if there's nothing in the list then either your card is too old or just doesn't have proprietary drivers available for it from the manufacturer.
tmadden: You could try Linux Mint with MATE desktop environment too just on the off chance. It's a fork of the old Gnome 2 environment and might use an older version of X.Org, it's perfectly functional and some people prefer it as it looks and feels just like the old Linux. Or for that matter you could also try Linux Mint Debian Edition which uses only 100% stable packages and might use an older X.Org too (but less likely). Linux Mint with Cinnamon uses Gnome 3 with a nice shell but would give you the same issues as Ubuntu which uses Gnome 3 with the Unity shell. Linux Mint is heavily based is heavily based on Ubuntu and uses most of the same repositories and feels very similar. Might be worth trying first before buying new hardware.
gzt: What is the exact brand and model of pc you have?