"I couldn't find a database server on 'localhost': A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond."

This is as far as I've gotten with trying out SilverStripe via EasyPHP in Windows. I've created a database in phpMyAdmin, and the user/pass are correct, but silverstripe doesn't seem to like it...

The answer to that problem might lie in your HOSTS file. Sometimes a computer will have two address entries that refer to the local computer. I haven't looked into it enough to find out exactly why, though I'd venture to guess that it either has something to do with IPv6 capability, or having two network cards (such as a laptop with a wired and wireless connection). This dual entry might be what's causing the issue, particularly if localhost isn't mapped to 127.0.0.1 (in which case, it's possible it's mapped to 127.0.1.1).

There's also a chance there's no host listing at all. If that's the case, then you can add a listing for localhost and then references to localhost should work as expected.