php disconnect(); and site running slow?

My art site: http://www.okanaganeroticartshow.com is/was running really really slow.

Godaddy is saying it is because I have scripts that are not closing – here is their text from a number of different emails back and forth:

>>However, when navigating there is definitely a slow load. This is usually caused by open database connections that can be closed out in your scripts.

and in another email:

>>WordPress is an application that utilizes PHP language. It’s always good coding practice to make the query, return the data and then close the connection as soon as possible. With your situation, the connection is not being closed and thus your site is taking far more time than it should to load. You can use the following function to close the database connection:

disconnect();
(end email quote)

Now I don’t profess to be an expect, god knows, and I want to make that clear here too. Wanting to know what there is on this subject on the net, I googled disconnect(); +php and one of results is found below:

http://stackoverflow.com/questions/336078/php-mysql-when-is-the-best-time-to-disconnect-from-the-database

My understanding of these comments is that use of disconnect(); can be a real pain in the butt. That a page when finished loading will disconnect automatically (is this right?) and therefore disconnect(); is really not necessary, it can cause more problems that it is worth.

So my questions are these:
1. how can I find out which scripts (I only use plugins) are the problem (whatever that problem may be)
2. how can they be fixed to speed navigation?

Hoping that makes sense.
Thank you very much! Julia