Can't use Live Gold Membership to get free Sonic Generations

You'll want to go to http://live.xbox.com/accountmigration and migrate your region to NZ. Sometimes the 360 system sees accounts has being in a different region
even if everything else shows it as being correct.

100% fixed my son's issue, 360 has an initial problem with first time crossover downloads as all regions are set to US so has to be migrated to the users region by following the link.

You'll want to go to http://live.xbox.com/accountmigration and migrate your region to NZ. Sometimes the 360 system sees accounts has being in a different region even if
everything else shows it as being correct.

Thank you. I tried that too. But still won't download. I hit the green download button and nothing happens.

Its not necessarily that your Xbox thinks you're in the US so much so as it is that in order to claim some free games off of Xbox Live, such as the Xbox original and Xbox 360 titles when they go free with Gold, you do actually need a valid billing account
set up with your Xbox. I know that kind of subverts the whole 'games being free' thing but that's just kind of how it is for some reason. The games are one hundred percent free, you just need a valid billing account for that 'credit' for the game to go to,
or something like that, its pretty tricky to explain.

First thing to do, would be to go to your region/location settings and just 100 percent reconfirm that your information is set to the New Zealand market. Then, go to https://account.microsoft.com/billing/payments
and add a valid billing account to your Microsoft/Xbox Live account and you should be able to download the free Xbox 360 game once that information is processed and updated.

I know it kind of sucks to have to go through that hassle to get a free game, but I'm pretty sure that'll fix it.

Yes, I did check and that was correct.