I have been able to get the Google Checkout merchant calculated shipping to work on our webstore. If you describe in more detail what is wrong I might be able to suggest ways you can fix it.
Some quick tips to help find out what is wrong:
1) You can check the intergration console in the Google Checkout dashboard.
2) You can check your URL is available by doing:
wget --post-data=blah # (or your own favourite method of POST'ing)
3) You can view the inbound/outbound Google checkout XML messages in the database table
So for example you might run:
select max(debug_id) from googlecheckout_api_debug; -- To determine the last message id
select * from googlecheckout_api_debug where debug_id = X\G -- For values of X just under and equal to the max id
(FYI the \G just makes the formatting of the XML a little easier to read from the mysql command line, if you use a graphical tool then that won’t be a problem for you.)
Edit: I wrote these instructions more completely with screenshots and example output, hopefully it’ll be useful to you.