Ok,I think it is going to be best to install a new 3.1.10 board on the new server first.
1. create a working folder on your computer, name it "working" or whatever.
2. click here and save to that working folder:
3. unzip the package to that working folder.
4. using ftp, upload the folder named phpBB3 to your new domain server.
5. in your browser, go to: http://threespiressearchsociety.com/phpBB3
and run the install.
6. using ftp, delete the folder named "install"
you are done, you now have a brand new phpbb 3.1.10 board at
once you have that done we can move on to the database problems.