First of all, you can get older versions here.
Second, there are a number of reasons that the upgrade may have broken. I suspect that you may not have confined your mods to the wp-content directory, or that you are relying on a plugin that can’t handle the upgrade. I had to delete all my admin theme plugins because they broke when used with other plugins. I stick with the vanilla admin theme.
I do constant backups of the DB and source. If there is a problem, I can always revert. I recommend that you follow a similar best practice.
If you do an upgrade, logging into the admin should invoke a DB upgrade. In many cases, this is simply a version change, but it could be more comprehensive.
Again, I cannot say this strongly enough: USE THE wp-content DIRECTORY FOR ALL YOUR MODS! It’s quite possible to do radical changes to the appearance and operation of the site without hacking the core. Also, even if you do stick with the wp-content directory, you could rely on internal calls that may not survive upgrades.
Also, be conservative with which plugins you use. Plugins may not survive upgrades very gracefully, especially big upgrades. A good example is what happened to the Role Manager plugin. It broke in 2.2. Luckily, a German guy took it over and applied a fix. Plugins can also step on each other. I had to remove the wp-sticky plugin because it stepped on the event calendar 3 plugin, and I decided that I needed events more than sticky posts.
Good luck.