The reason that Goodreads or any 3rd-party service asks for access to your address book is to find other friends/contacts that use the same service.
Using basic authentication, people would just provide their username and password to the service (say their Gmail account) and the service would read the address book. This is a highly insecure practice and is teaching people to be phished.
The new method that Goodreads is using is OAuth or OAuth 2.0 which provide granular access to your accounts via a token, and allows access to be revoked. In theory this is better, in practice a nefarious user can get that password in a hundred ways.
Once Goodreads has access to your contact info, you have to trust them that they won't do anything dodgy with it, like spam your entire address book (Plaxo, I'm looking at you!). If you're not comfortable with this, don't grant access to them.
According to Google Support you can use the recovery link on this page: Recovering sign-in information
![Forgot your username feature](https://i.stack.imgur.com/ezBaf.png)
From here, you should try with all accounts you are associated with to see what accounts are linked. (Assuming you remember all email accounts used apart from the one you forgot). It is sort of hit and miss but it has worked for me on two separate occasions.
You should get an email similar to the following.
Your recovery address, phwd@gmail.com, is associated with:
xxxx@gmail.com
xxxx@gmail.com
xxxx@gmail.com
xxxx@gmail.com
xxxx@gmail.com
To sign in, visit the link below.
http://www.google.com/accounts/
If you've received this mail in error, it's likely that another user
entered your email address by mistake while trying to recall their
username. If you didn't initiate the request, you don't need to take
any further action and can safely disregard this email.
If clicking the link above does not work, copy and paste the URL in a
new browser window instead.
Thank you for using Google.
For questions or concerns regarding your account, please visit the
Google Accounts FAQ at http://www.google.com/support/accounts/.
This is a post-only mailing. Replies to this message are not
monitored or answered.
As seen above it works for multiple accounts. So any account that has phwd@gmail.com listed is brought up in the list.
Additionally you can search your email accounts for the following subject line
Your Gmail address has been created
This will bring up (if you didn't delete it), the confirmation email messages of all Gmail accounts you used the current account as a recovery point. Although, based on "used in ages" I am not sure how far back Google used to send out this message.
Best Answer
Try on another browser, if same problem try it on other device and check that you have right username and password.