Don't use PHPmyadmin. For anything. Ever.
Even though 150M is quite a modest sized database, I think it's unlikely that PHPmyadmin can correctly backup or restore such a DB.
Have you tried manually loading it (using the mysql command line client) into a local instance of mysql to check that the backup is in tact?
When you use mysqldump, you'll get a file which is basically a sequence of create table and insert statements etc (depending on what options you chose).
You can then compress this file, transfer it to the new host (by whatever file transfer method you prefer - if using Linux/Unix, I'd normally suggest scp or sftp), then uncompress it and load it into the database by piping it into the mysql command line client.
mysql (whatever options you usually use to connect to the database) < backup-file.sql
Note that on some Windows systems, shell redirection may not be binary-safe. Check it first. I'm not sure what the alternative is.
Mark
