Very silent piece of audio. Compressor or???

Hello everyone.

I am new to audacity, so that is why I probably have no idea what to do.

I have read couple of notes about the envelope and compressor and even tried to normalise, but so far I haven’t had much progress. On the contrary, I have had only ‘jangling’ loud sounds and very silent those, which are silent. I attach here the screenshot of the recording, so that you can see the difference between the loud and the silent peaks.

Can you recommend anything?
Screen Shot 2017-11-06 at 10.43.31.png
If you make the very quiet sound much louder inevitably it will then be of lower quality than the un-amplified audio: more hiss, more conspicuous (jangling) digital artifacts. That’s unavoidable.