Not sure how much you want to worry about it, but since I work for ASUS, I should suggest you get the adapter sold through ASUS to be safe, but yes, the G55VW and G75VW use the same 180W adapter as the G75VX, so if it works for those other models, it should work for your model too.
If you are worried about it, you may want to check with your local ASUS support or stores about finding the 180W adapter which is also used by some newer models like the G750JX and G750JW.
http://www.asus.com/support/callusThe 90W adapter (19V*4.74A = about 90W) you tried is too small for your notebook although if you leave the notebook turned off, it may be able to charge the battery at least.