I have tried logging in with my Launchpad ID. But it shows me as a totally new user, with rep of 0.
I don't want to lose the rep I have here.
Go to your profile and near the top there will be a link that says My logins.
It will show you all the accounts associated with you Stack Exchange account, and let you add new ones and remove old ones.
Here you can add your Launchpad account and remove your Google account.
Moderators can also do this, and one might beat you to it :)