Trying to find PRODUCT KEY of Red Faction Guerilla in registry

So, like I posted in my previous post about Red Faction Guerilla, I still have the game installed. I have long since finished it even before the first patch came out. But now I cannot play it. RFG_Launcher stops working all the time (link). Installed both updates manually, not through GFWL because of this.

But I have since found a possible solution thanks to Mr. Pelvist from the first link.

My problem now is where in the registry can I find the product key of RFG? I tried searching Vista's registry via regedit. I have found several Red Faction Guerilla and Volition Inc. entries. But no product key.

Any ideas? Is it even there?

The DVD is with my cousin, and so is the manual, etc. So telling me to get the product key through that is useless because my cousin has become next to impossible to get a hold of.