I have finally got everything worked out with the new server. I almost lost my Movable Type mysql databases on the old web host. After fiddling around with different control panels I finally managed to get a dump of the old databases using phpMyAdmin. After that I uploaded the exported sql using MySQL Control Centre. Thank god for some excellent open source tools. Thanks to all who work on these tools, you saved me lots of work.
If this post works, it means everything is back to normal!