If you import it into burning software you should get an option to edit the file and you will see a waveform of the whole mp3 with the dead or quiet bit in the middle. Select the first track and save as a mp3 then go in again and save the second track too. You can do this with nero and winoncd. I've used it to seperate live recordings that I recorded to minidisc in the past.

You can also use an audio editor like soundforge, Acid, Magix muzik studio, Recycle etc. as they can usually import files as MP3 rather than just .wav or a proprietary format. Its the same idea as the waveform editor you see in the likes of Nero but you get a lot more control, plus you can do nice little things like volume levelling and filtering out noise. Handy for cleaning up live recordings or recordings taken from old vinyl. Most of these programs are pretty expensive but I'm sure theres a few free (and legal) ones if you look on sites like Download.com. If its just a one off thing you want to do you could probably use a 30-day trial version.

goldwave, is a good free editor, lets you select exactly where you want to cut etc also has some nice features, like revers, pan, fade and so on