cannot connect remotely unless logged on locally

We have several XP computers in our lab. One of them behaves strange: I
cannot connect remotely to that machine, unless I first log on locally. After
that it is fine, even if I log off. Also I cannot restart this specific
computer remotely. If I type in the command line "shutdown /r" it gives me a
dialog, saying that it will be shut down in 30 seconds, but then nothing
happens.

All other computers behave well: one can restart them remotely and after
restart it is possible to connect remotely without logging on locally.

What could be the problem?!

Viktor