Are you using the hard-float or soft-float wheezy raspbian? The soft-float version seems to be problematic on some Pis. See Soft-float version of Raspbian does not boot.
Another possibility is a problem with the SD card. There have been reported problems with using large cards.
Also, check that the SD card is properly seated in the slot--I had a similar problem when my card wasn't properly connected.
Update: Validate that you have correctly burned the SD card. Do this by mounting the SD card on a windows machine (i.e. plug the card into an SD card reader). Using Windows Explorer, browse the SD card. You should see several files including one called cmdline.txt. If you cannot see such files then you have not burned the SD card properly.
A common mistake is to not unpack the downloaded wheezy image. It's delivered as a zip file, so unzip it. There will be an .img file--this is what you want to burn.
Update: Try this troubleshooting wiki.