Help.my 9 week old puppy howls all night when she's left in the crate, shall I let hr run around downstairs?

We have had her over a week and tried leaving the radio on, but as soon as we leave her she starts.When I get up and let her out of the crate she settles down and goes back to sleep. After a week of sleepless nights and worrying about the neighbours, does anyone think if I give her the run of downstairs, it might solve the problem? She goes in and out of the crate during the day, but as soon as we shut the door she starts howling. We let her out and she settles down under the table. I really am at my wits end and although I love her dearly am seriously thinking of giving up and re homing her. HELP?