"I do not hear much."
'ascoltare' generally involves an intentional act on part of the listener. So, most of the time 'to listen to' is a better translation than 'to hear'. Without a specific thing you're listening to, 'ascolto' sounds strange to me (not a native speaker). I'm sure siebolt can give you a more definite answer.
I'm not an italian nor english native. Even so, my language is more closer to latin language than the english is. So, just to understand the expression: "Non sento molto" sounds to me like "I'm not sorry" wich is very rude. Is this a possible translation, considering "sento" as emotional feeling?