The circuitry which provides the sound in the projector/transmitter unit might be separate to the circuitry for the light and transmitter function. If the batteries are rather low, there might be a sufficient voltage for one function to work but not for the other. Poundland will sell you 6 AA alkaline batteries for a quid, so it's not going to cost a fortune to put a new set in. (Each unit takes 3 AA batteries. If there's not a Poundland store near to you, Wilkinsons also sell AA alkaline batteries, under their own brand name very cheaply. Make sure you get alkaline batteries; zinc chloride ones will go flat almost as soon as you put them in).
Once you've got a new set of batteries in, you should quickly be able to find out (by trial & error) whether everything is working as it should. If it is, 'baby sounds' should switch on the projector unit rather than lighting anything up on the receiver (although, obviously, those same baby sounds should be heard through the receiver). That's based upon reading the product description, here:
http://service.mattel.com/us/productPopup.asp? id=G4120
Batteries don't last long in devices designed for transmitting radio signals. They also go flat quite quickly if left in unused devices for many months. So it's quite likely that your problem is simply related to old, tired batteries. If not, it's time to complain to the vendor and/or to eBay.
Chris