Windows 7 Starter, which is the OS installed on this netbook, doesn't seem to allow access to multiple network shares, with different credentials. One has to disconnect from the currently connected network share before connecting to another one.
Disconnecting from a network share that's been mapped as a network drive is easy enough (the menu item to look for starts with 'Disconnect' ...) - but there's no obvious way to disconnect from a network share that has not been mapped as a network drive.
I found a solution on this forum thread - run the following command in a command window:
net use \\MACHINE\share /dwhere you should replace
\\MACHINE\sharewith the path of the network share you want to disconnect from.