All connections fail, 10061

I came in to work this morning and none of my MySQL connections would work in HeidiSQL. All of them instantly fail with 10061 'Can't connect to MySQL server'.

Yes, the servers are running.
No, I'm not blocked by a firewall.
Yes, the user@host has valid permissions.
Yes, I'm using the correct username and password.
Yes, I've restarted HeidiSQL many times.

If I fire up MySQL Administrator on the same machine and plug in the same hostname, username, and password it connects successfully. However MySQL Administrator is crap, and I need HeidiSQL because it saves me a boatload of tedious work.

Help?

10061 is a low level error (winsock "connection was refused") that a TCP/IP connection was actively refused by the server that mysql is on. that is happening before permissions or username/password come into play, ie the error is on the network level.
it is really strange that you can connect to the server with the other program, but get 10061 with heidisql.
i must admit i have no idea how to handle this one.

PS: in such cases, after trying telnet.exe and "open servername 3306", with mysterious network problems i usually use wireshark. this is admittedly not really simple, and probably overkill, but it shows me exactly what is going on on the packet level, which nearly always helps to solve the problem.