Now is the time to adjust the level of the recording. Nearly all audio software will allow you to adjust the peak volume of the file accurately. Select the whole recording and choose 'Normalise' from the Amplitude section of the Transform menu. Set the level to something in the high 90s (I use 98%) and click on OK to set it off.
By now the recording should be in pretty good shape. Zoom into the beginning of the recording again. Now that the noise has been removed, it should make it a lot easier to trim the 'silence' from the beginning and end. Turn up the volume and check that you have not inadvertantly taken any of the actual songs. (Note that sometimes tracks do seem to end abruptly, as the original engineer or tape operator may have made poor choices. If this is the case you can always choose a volume envelope to fade the track out if it is noticeable).