Answer
Two things worth checking beyond DNS/hosts-file causes: disable a separate always-on VPN client (like Global Protect) if one is running alongside whatever VPN you're using to reach the environment — having two VPN clients active can specifically block Developer Studio's first-time connection attempt even when other tools connect fine; and make sure the database password was copied using the Build Place page's dedicated copy button rather than a manual Ctrl+C selection, since a manually-selected copy has been known to silently include extra characters that break the connection. See also DNS/hosts-file causes of the same "too long" error.