Okay there are a few ways to skin this so to speak. First get the IP of your new server. Run a ping using a tool like Just Ping. There you can see your global ping times. This will give you an idea on how long it takes to connect to your server from large cities around the world. Ten for more information you'll want to use something like Pingdom Tools to get a waterfall view of exactly what is taking so long to load. Use your larges page there using your domain name not IP. This will give you a pretty good idea of where your bottleneck is. If the site is the same as the other, you may want to consider looking at your .htaccess file and making sure you copied over the settings. A good way to see if the problem is related to your host (Media Temple) is to ask them for another site on your server to test the load time, and run that through pingdom tools.
If the problem is you host you may want to consider switching to a different hosting company. If the problem is not the hosting, and lets say that you are getting bad ping times because you are far away from your host, there are a few approaches. A good practice is to parralelize downloads across hostnames. I would definitely also recommend using a CDN such as CloudFlare, which is easily accomplished buy using web hosting from a cloudflare certified partner or using it directly from CloudFlare, in which case you may will have to update your nameservers. As long as your host is providing a fast connection and the load on the dedicated box is low, then the main problem is that you are to far away from the host. One thing that can help with this whether or not you decide to use a CDN (which I recommend for global load time reduction), is to parrallelize downloads across hostnames. This is due to the fact that most browsers will only make 2 simultaneous connections to a given hostname. This means that if 50 resources are loaded on a page that the browser will do 25 pulls. If the connection takes 200ms, times that by 25= 5 seconds plus the time to download the resources.
Now if you load the resources from multiple hostnames i.e.
Then you are only loading 10 resources from each hostname and the browser only has to do 5 pulls = 1 second plus download time.
A CDN will of course reduce the time that it takes to do those pulls.
You can use CNAME entries pointed at the root domain to create these hostnames without maintaining multiple copies of the resources.
I hope that gives you a step in the right direction to getting your global page load times under one second.