Weird. There are 6 workstations and all but 1 can connect to SQL Server using the exact same connection string. So the SQL engine is obviously running and the issue is not centralized at server level (e.g. "Allow network connections to this server", "Maximum number of concurrent connections", "Named pipes"). Checked the firewall on the station and it's OFF at all levels. Even tried to add incoming and outgoing firewall rules for TCP 1433 and UDP 1434 with no effect. I tried to connect using the IP address of the server instead of its name in case there might be a name resolution issue between stations, but nope.
What else should I be checking on that workstation?