Another possibility is AF is set to single servo, focus priority and you haven't achieved focus. I had a miserable time last evening with a similar setup (D300, even so) in a dark room trying for a self portrait. Who knew focus points could be so small and so easy not to stand in?
I thought I would physically test this with a Vello wired remote and was a bit distressed to find it was doing the same thing. But, as it turns out, for good reason. The connector/socket duo is quite tight and I had not seated the connector fully. With a little extra push, things went back to expected.
I have the Giga T Pro II also and use it with my D600 and D800. There are three cables provided with the Giga T Pro; two look very much the same, but are different. I believe one works with the D7000, and the other works with the D600. I mistakenly used the D7000 cable first and had the same symptoms you see (lights work, no shutter release). When I used the correct cable, everything worked fine.