If you searched a little more, you found an article (it was probably at Ubuntu Wiki or something close to that) that tells you to use the graphical (software) update tool with a special switch (launched from the command line), which makes the update tool upgrade your whole Ubuntu version, including editing the sources file.
sudo sed -e ’s/\sdapper/ edgy/g’ -i /etc/apt/sources.list
That's dapper -> edgy. If you want to upgrade to feisty, and you're using dapper, you need to upgrade dapper -> edgy then edgy -> feisty, which in my opinion takes a whole lot of time and can cause a lot of trouble (or then not, who knows). I'm not sure if Dapper has this "web upgrade" functionality really working, I think it was only in Edgy that it was "supported". It still probably works, yes, but things have changed between the versions and you are likely to get some trouble that you need to fix manually. For the sed command, read
to understand what it does and then why it doesn't work for you..it's probably just faster to go trough the file manually, there are really not that much words..and you can use a regular text editor with search&replace and replace every "dapper" with "edgy" (and later on "edgy" with "feisty" - you can't probably do this directly "dapper" - "feisty", but need to do it one version at a time), and it should work almost as easily as with sed.
Well, like I said, it's going to be a hard process. It takes time to load all the stuff from the web, twice if you want Feisty, and if your network happened to get cut in the middle of it (or some packages trashed), you would have to start it all over, cleaning the half-done upgrade traces first. A friendly advice: only do the downloading once, like you did with the Feisty disc, find out why it won't work properly (I'll have one advice lower on) and do a clean upgrade, along with formatting of your root and boot partitions, and have tons less trouble, plus spare a lot of time.
Why the Feisty disc won't boot..well, there can be a number of reasons, but I'd start off with video card. It's the most common reason. It's rather easy to ensure that; first calculate the md5sums and ensure they're ok (if you can, for the image you burnt the disc from, and if it's ok, then for the disk itself -- there should be md5sums on the disk also). Boot the disk and from the prompt hilight the "safe graphics" option (second topmost, if I'm right). Don't boot it yet; at the bottom of the screen you see some Fn keys along with their explanations; use the Fn key mentioned there to set your resolution to some very low (vesa-compatible) value, preferrably 800x600x16. Then hit the other Fn key that lets you edit the kernel commans before booting (you should now have the safe graphics boot line hilighted from the menu, before editing); alter the line by replacing the word "splash" with "nosplash". This disables the graphical loading screen, allowing you to see boot messages. The low resolution, on the other hand, ensures that your resolution is not causing trouble. Now hit enter to boot, and see if it gets farther..it did for me, on several machines that had this kinds of problems (no idea why graphics card/drivers can cause that many different kinds of problems, crashes and errors, but it seems they did..after setup, everything worked fine on high res).
Another trick to try is simply to download the Alternate install disc. It allows for text-mode installation, thus passing by possible graphics trouble during setup; after the setup you can configure (unless the setup does it for you already) your graphics devices, resolutions etc. as much as you want, but anyway the hardest part can be passed because during the setup you can't do too much magic with the graphics settings.
Software upgrade (trough package manager) might be "supported" by Ubuntu (I know it even notices you there's a new version, in Edgy and later, and asks if you want to upgrade to that), but it's still not half as good as a clean install from a setup disc, formatting the root and boot filesystems (if you have separate /home, don't format it - keep your settings and files); that ensures your system is installed properly, there are no traces of the old system messing things up, and you need to spend less time downloading.