ZDriver.com - just got my first Z!!!

hi im new but i have just bought my first new Z and i have a few issues with it but one is getting annoying. My gas gauge does not work but the light does sorta. i was driving the car all day with no issues she was starting right up but the last time i tried to start her nothing was happening. All my lights where coming on and i can hear the car turning over so i was like hmm why is it not igniting omg gas. so i put gas in the car good do go. now today i was going to work she started up lill rough this morning but she did start so i went to a friends house. As i was trying to leave guess what would not start????? same issue out gas in her started fine. i just put a full tank yesterday. I tried to fill it up today only added 2g to the car before it topped off. so i know the car has gas. Im thinking its something with the fuel system? Any ideas?