Apache MySQL Performance dip

Separating the MySQL and Apache servers has slowed my site down, instead of speeding it up! Any suggestions?

I have hosted a LAMP website on a 2GHz AMD Opteron server running with 2GB of RAM.
As the data needs grew, the MySQL database seemed to need its own area, and could not serve the apache server fast enough.

So I split the MySQL database to run on its own 2GHz AMD Opteron/2GB RAM server - with a single-hop connection between the two of them at the data center.

But performance has dipped - any clicks take a much longer time to show a result from the database.
Any ideas how to get better performance from the separate Apache/MySQL server setup?

Thanks!