I do believe the G73sw has a total of 4 ram slots 3 being visible under the removable cover but 1 being under the keyboard. Manufactures (especially asus) do not lockout ram slots. either the ram you got is DOA or something is just not right with the installation. make sure you have the battery out and the power cable disconnected when trying to upgrade the ram.
I've noticed that some G series asus laptops have ram slots under the keyboards. this would require a tear down just to upgrade the ram. IMO poor design but what are you gonna do. if you have to do a tear down (take it to a shop or asus retailer if you really don't know what you are doing) do a ton of searching and watch some youtube videos. see if you can get your hands on a service manual too.
G73SW ram specs:
DDR3 1333 MHz SDRAM,4 x SO-DIMM socket for expansion up to 16 G SDRAM (Quad Core),2 x SO-DIMM socket for expansion up to 8 G SDRAM (Dual Core), *2
http://www.asus.com/Notebooks_Ultrabooks/G73SW/#specifications
Desktop:
Motherboard: ASUS ROG MAXIMUS VI EXTREME
RAM: 32gb Ballistix 1866 DDR3
Chip: Intel Core i7 4770k OC'd Stable 4.8ghz
Water Cooling: Corsair H110i
Power: Corsair 1200i
Video: Asus STRIX OC'd GTX 980
Primary Hard Drive: SAMSUNG Pro 256gb SSD
55" Vizio HD display
Audio: Logitech Z5500
File Server: Dell Poweredge r710 1.3TB Hard Drive Storage 128gb RAM
Storage SAN #1: Dell Equallogic PS100e 14x 750gb SATA
Storage SAN #2: Dell Equallogic PS5000V 16x 1TB SaS
