The final conclusion-response of both:
--- gmail-imap.l.google.com ping statistics ---
10 packets transmitted, 9 packets received, 10.0% packet loss
round-trip min/avg/max/stddev = 21.864/23.304/29.316/2.224 ms
--- gmail-smtp-msa.l.google.com ping statistics ---
10 packets transmitted, 10 packets received, 0.0% packet loss
round-trip min/avg/max/stddev = 21.740/24.515/28.501/2.456 ms
Wow, you've gat a fast connection!
Do you have any Protection Software installed, like AV SW, Net Nanny/Minder?
See if this helps...
Open Keychain Access in Utilities, use Keychain First Aid under the Keychain Menu item, then either check the Password under that item, change it, or delete it and start over.
Resetting your keychain in Mac OS X...
If Keychain First Aid finds an issue that it cannot repair, or if you do not know your keychain password, you may need to reset your keychain.
Whew, have you reset your Router or Modem?
Try putting these numbers in Network>TCP/IP>DNS Servers, for the Interface you connect with...
Then Apply. For 10.5/10.6 Network, highlight Interface>Advanced button>DNS tab>little + icon.
DNS Servers are a bit like Phone books where you look up a name and it gives you the phone number, in our case, you put in apple.com and it comes back with 18.104.22.168 behind the scenes.