I have a customer who is moving a site to my services.

This site had several databases in it and when I checked through PHPMyAdmin his databases were empty.

I believe the issue is the old server is running a higher version of MySQL, but since we do not have Root access to it I cannot be entirely sure.

I have pulled files from PHPMyAdmin but I am not sure if the MySQL info is accurate. Anyway, I am having a lot of trouble importing the files. I have modified them a little bit, but each step of the way I hit a bump in the road.

My server is running on the local host 4.0.27-Standard and on the PHPMyAdmin Client Version 4.1.22-Standard

The other server is running on the local host 4.1.22-Standard and on the PHPMyAdmin Client Version 4.1.22-Standard

Additionally I am running PHPMyAdmin 2.11.0 while the old server is running 2.11.6

Can these be the problems or is it something else? Everyone says PHP Version is not the problem, so, I'll start here.

What errors are occurring? Do you have command line access to use mysqldump?

Depending on the size of the MySQL databases, backup and restoration via phpMyAdmin probably isn't the best way to go about it. MySQLDump via SSH is the most effective way of backing up and restoring a database, not only to ensure all the data is backed up correctly, but to ensure the data is restored completely.

If you have SSH, or can have SSH enabled on the other server, using MySQLDump and WGET to pull the database over would be your best option.

That said, if phpMyAdmin is your only true option, again depending on the size of the databases, you may have to backup the databases in pieces instead of as a single SQL Dump.

phpMyAdmin will allow you to backup XX number of tables, then another XX number of tables at a time to reduce the size of the full dump.

My server is running on the local host 4.0.27-Standard

The other server is running on the local host 4.1.22-Standard
That's your first problem. (Isn't it about time you upgraded MySQL?). To get a working database dump from phpMyAdmin go to the export page, look for the "SQL compatibility mode" option and choose MYSQL40.

If it's a big database you may still have problems as WPSensei describes.

I would do an export from phpMyAdmin as suggested by the above member.

I really hope you find your solution using PHPMyAdmin. Would suck losing all that data.