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Upgrade to 1.7 from 1.6, now the API is not working
The first important thing to consider while migration is to choose the best method for it. Connect Manager is one of the best, and it is a rare occasion, when it is something wrong with it.
I would also sagets to take a look at upgrading via FTP. It is understandable enough, but to start with, make sure you take a complete backup of your Magento website.
Than, create a directory in your Magento install and name it with any name you want to use.
Now upload Magento 1.7 files, into newly created directory i.e. TEST
Create a new MySQL database with new username for your Magento website.
Import the database (Backed up in step 1) into this newly created database.
Modify the core_config_table base_urls to point to your test location, e.g.www.store.url.com/test/
In order to use new database, you need to modify app/etc/local.xml
In the end of the way, just run the frontend and backend of website.