I read various posts on many sites with people having the same problem in Windows XP or Vista and a registry fix which was even suggested by Microsoft to solve the problem, alas though I'm using Windows 7 and this didn't work.
After much chin-rubbing and head scratching I found the answer!
Go into your VPN's connection properties and into the Networking tab. Go into the properties for IPv4 and click on Advanced. Go into the DNS tab and enter your DNS suffix in the box near the bottom labelled 'DNS suffix for this connection'.
The next time you connect you should find you can now ping/access hosts using just the standard hostname.