Do you mean you're having trouble registering with Google and Facebook within Shopify or just in general? If your Google account has been suspended that is something you would need to reach out to Google about directly and not something Shopify can assist you with. You can reach Google's help centre here.
In terms of looking at your store to see what might be going on, this would involve taking a look at your store admin to understand better and investigate. Because we'd need to access your account in order to understand better and resolve. While we’re not able to provide account-specific support via the Shopify Community at this time, we’d be happy to continue assisting you through live chat, email, or callback. Please visit our support team here and log in to your account to create a support request.
Nick | Community Moderator @ Shopify - Was my reply helpful? Click Like to let me know! - Was your question answered? Mark it as an Accepted Solution - To learn more visit the Shopify Help Center or the Shopify Blog