Need help with resources timing out please

I recently took over a site (fidkids.com). They asked me to take it over because it was performing really slow and going down. So I have begun using WPMU plugins to make it better. I have come up against another issue though.
I have been receiving the max connections error (max connections are set to 30). I installed the query monitor plugin, but I cannot seem to figure out what is causing the issue. The host (GoDaddy...ugh!) has not been helpful at all and I believe they have contributed to the site's issues.