The migration is complete and we are now up and running on the new server. This server is "semi-dedicated", so there should be less sites hosted on this server, and we get more CPU power and more allocated memory. In addition to the move, I believe the issue of the refreshing is now fixed as well, although it was an entirely different issue.

Should anyone experience any issues, which I did at first and fixed already:

-Delete your cookies and cache aka temporary internet files.

Please update with any other issues you may have in this thread. Hopefully we won't have any and we'll be smooth sailing on this server!