Well it doesn't make sense to me that Coinbase would take out all the contents of your account except for 0.00002 BTC. In my opinion it looks to me that you only have around 0.00002 BTC in the actual account, and you just inspected the element of the webpage to get it to look like 300~ BTC.
Plus, may I ask why you said in the OP that you had around 700 BTC in your account, whilst the screenshots only show around 300~ BTC?
Coinbase is a registered company, so I'd say that you have a better chance of chasing down your funds than an anonymous bitcoin exchange if the same thing happened, like BTC-e exchange.
That is, if your screenshots are real and everything you're telling is legit here. I strongly doubt that.
I do not need you to believe, could not get me to give you the email and password login, I do not have time to play around, I have the Video Record transfer funds account blank, and there appear the number of BTC significantly, for the sake of the security of my data, I will not show to the public the video.