Recurring database errors when importing

I am trying to update an old site currently on wp3.1.3 and due to it’s size I have been putting if off until now;because the client wants a restyle of the site. I have been trying to upgrade the database to mysql5 from 4, I have tried exporting the database now 8 times and keep getting errors. I have followed the instructions on the codex about backing up your database and followed them to the letter. I am using phpMyadmin to do this, the database is hosted by Namesco, the latest error is below. Please help, I need to update this site asap.

SQL query:

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— Database: zenithcosmet
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— ——————————————————–
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— Table structure for table wp_commentmeta
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DROP TABLE IF EXISTS wp_commentmeta ;

MySQL said: Documentation
#1046 – No database selected