Liightroom 3 is six years old, and there's really no reason to buy totally oudated software.
Did you buy it on eBay? Then there's a very high risk of it being pirated software, and you could well be getting malware that could cause great harm to your computer.
The reason that the serial does not work, is probably that it has been used for piracy, and is blacklisted by Adobe.
Contact eBay, or wherever you bought it, and get a refund.
Then buy the latest version from Adobe, which you can do here: Products