Just a quick note so you're not concerned, after you have sent all the resources, supplied the workers and power, and it starts construction, it can take a long while to finish. Do something else in your city and just let it run. Don't enter any other cities until you get the message to "cut the ribbon" and it opens.
I've never built the international airport before, but with the arcology and solar farms, it can take up to a Sim-week to fully construct depending on regional traffic and server lag and stuff. Stay in the city that completed the GW until you can see that it is working. Then, if you're the mayor of any other cities, you can enter the others connected to the GW. At first, it will look like it hasn't been built. Don't worry, you will eventually get a message that it is constructing, then a "cut the ribbon" message, and it will be all good.
Whatever you do - do NOT try to start it again or send resources from another city. You'll totally bug it out and destroy your region.
