Then the problem is likely related to any of:
1. server firewall is blocking external communication on port 80
2. server PHP configuration has blocked/prohibited use of fileopen() calls to external sites
3. you've entered an invalid USPS user ID (password is irrelevant anymore)
You might get a bit of information by editing your /includes/modules/shipping/usps.php file as follows:
approx line 416:
a) remove the // at the front
// mail('firstname.lastname@example.org','USPS rate quote response',$body,'From: <email@example.com>');
b) change "firstname.lastname@example.org" in both places to your own email address
c) try testing some quotes
If you get no extra emails containing USPS quote data, then the problem is #1 or #2 above.
If you do get some emails with raw USPS data, post that data here.