This should fix your punkbuster errors or 'could not connect to server'.

If you still get these errors after doing this (which you shouldn't), then it's the server and not you.

Close BC2, and make sure it's not running in processes (sometimes it doesn't close).
Go to: ..\Steam\steamapps\common\battlefield bad company 2\
and find the 'PB' folder. delete it.

Go here:
http://www.evenbalance.com/index.php?page=pbsetup.php

Download the client and add bc2 like the link shows, then click 'Check for updates'.
It should start downloading the latest PB and then you're done.

During the first few days of release this problem would come back to me so I'd have to delete the PB folder again and re-update.. I haven't had to do it for a while now, but keep that in mind.

I hope this helps as it's solved this problem for a lot of people I've told.