Generally from experience phpMyAdmin screws up badly on exporting and re-importing large databases on those servers who's memory limit is set to 8Mb in the first place.
I know this for a fact as Ive done many already for tikihost.net clients.
To re-upload your database you must click on SQL on phpMyAdmin or even better use SSH access and the mysql command. If the new server is configured with a PHP execution time of 30 seconds then the upload process will fail.
There are some tricks you can do, but I dont have time tonight to document them. They mainly involve modifing the tiki-install.php to use the db dump generated from mysqldump command, or a successfull phpMyAdmin export.