I don't have a smartphone (I have a symbian with access to the Internet), or iPod/iPad. Are there any other ways for me to get an authenticator from Blizzard without paying $6 for the physical authenticator?
Other than a phone, your options would therefore be a tablet, iPod (touch), or the physical authenticator.
For those without such a device, the other answers propose alternative means. Android emulation may be a good way to go, seeing as you would still be using the official authenticator.
You can use WinAuth, which is a popular third party authenticator for Blizzard games. It's not quite as secure as the official means since if someone gains access to your computer they can use the authenticator, but it's far better than nothing(you could probably put it on a flash drive so it isn't always on your computer).
You can also use Googles development tools to emulate an Android phone on your desktop and then run Blizzards authenticator app.
An excellent write up of the process with links to the various needed downloads can be found in this blog post at Elitist Jerks