I am using Windows XP SP2 under Parallels Beta 6 and I can't use shortcuts like ctrl-c, ctrl-v and any other shortcut. Backslashes also don't work.
Check out this thread: http://forum.parallels.com/showthread.php?t=1030&highlight=Control This should solve your ctrl issues.
I've mentioned this problem in another thread long ago. There hasn't been a clear official response from Parallels about this issue, hence we only have that workaround for the moment.