Just to be sure you did it properly..
1) Upload the SAME version of vBulletin you are using now to your new server. DO NOT RUN INSTALL.
2) Backup your database on your old server.
3) Restore the database on your new server.
4) Log into new server and upgrade vB versions if needed.
See the manual for more complete instructions..
https://www.vbulletin.com/docs/html/moving_servers
It works flawlessly if you use that method. I've done it many times for many sites.