I followed your steps and opened a music file first before opening Audacity - the clicked on the "Record" button. Sound waves were barely visible and sound was faint on playback. I clicked on "Effects" and selected "Amplify" from the list. Sound waves displayed and sound was audible.
Next I opened Audacity before opening a music file. It played normally and recorded and played back normally.
Audacity is quite a complicated program to use and reading the manual may be of benefit:http://manual.audacityteam.org/o/
Since the sound is low when you try to record, you could have a look at the settings in Alsamixer to ensure that your soundcard has been selected as well as the PCM level.
Sound Recorder is not available in Linux Mint 16 Cinnamon but I recall having used it some time ago.
I have tried the" Effects" >"Amplify" and there was no change, when I am trying to record into Audacity good quality sound is coming out of the external desktop speakers.
I downloaded the Manual and couldn't find any help there.
I have no idea where to locate the Alsamixer or how to select the PMC level, I will be at a Linux Users group meeting tonight and will enlist their help using your
suggestions. I think the soundcard is the most likely cause of the problem but it is just getting too tech for my level of computer knowledge.
I will let you know if I get Audacity working, when and how .