Buried on a technet forum is a very important fact: you can get System Error 58 when trying to connect to a share on a Windows 7 computer, and the only cure is to REBOOT the Windows 7 machine, even though it may seem that the problem is on the other computer.
In my case, Windows 2003 would not connect. It would not browse to the computer on the network (as it had the day before); it had errors in the System event log; and NET USE failed, also with System Error 58.
Rebooting the Win2003 machine made no difference.
Connecting from another Windows 7 machine to the Windows 7 share WORKED.
The problem was only FROM Win2003 TO Windows 7.
And cure was REBOOT the Windows 7 machine; instant fix.