Warning: mysql_num_rows(): supplied argument is not a valid MySQL result resource in C:\Inetpub\vhosts\thepinflow.com\httpdocs\staff\checklogin.php on line 12
Wrong Username or Password

That is the error message I am recieving.

I was using another website to host a PHP/SQL website before,
currently located at: http://www.blackairplane.com/Pinflow/index.php
which works. When I copied all the files over completely and then tried
to run it on the http://staff.thepinflow.com/ site (under the 1&1
purchased domain), and try to login, I return the following error:
Warning: mysql_num_rows(): supplied argument is not a valid MySQL result
resource in

C:\Inetpub\vhosts\thepinflow.com\httpdocs\staff\checklogin.php on line
12Wrong Username or Password..

yet it all works fine on my other domain www.theblackairplane.com as mentioned above...

I really need help on this as I am paying 40 bucks a month and not
being able to use the site as intended. How could just transferring the
site over from one domain to the other make it not work?

How did you 'copy all the files over'?

What versions of MySQL are running on your original host, and on your new host?

There are a few things that can munge a migration, but knowing the answers to these 2 questions will give us a better idea of where to look.