Hi,
If the google checkout configuration is good and your server is accessible, it should be good.
The next thing would be to make other test using their "sandbox".
Google checkout would confirmed order using "server to server" and HikaShop would set orders as "confirmed" (you would see the validation in the order history), mails would be send, HikaSerial would generate serials, etc
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.