Go into your PM system and click 'Outbox' this will give you a list of all the messages you have sent - have a look if it's listed, if not, then no it hasn't been sent. When you send a message you should get a confirmation screen telling you the message has gone and to whom. Also, on the left side of the message list in your outbox are some blue envelopes. A light blue one means the message has been read and a dark blue one that the message hasn't.
Sounds like you're using Mozilla Firefox as your browser. If so, I've noticed that if you type a PM and try to pre-view it, occasionally it will just clear the message box and you have to type it all over again. Really no point pre-viewing anyway as it's virtually identical to the message you've typed.
Messages aren't usually transmitted unless you click the Post Reply or Post Message button...............
As Trace points out above, check the person you wish to message has the PM facility by going to a post they have made and looking at the buttons along the top of their message. If there is no PM button, they cannot receive a PM from you...............