Why won't Mozilla let me use google?
Message: This Connection is Untrusted You have asked Firefox to connect securely to www.google.com.au, but we can't confirm that your connection is secure. Normally, when you try to connect securely, sites will present trusted identification to prove that you are going to the right place. However, this site's identity can't be verified. If you usually connect to this site without problems, this error could mean that someone is trying to impersonate the site, and you shouldn't continue. This site uses HTTP Strict Transport Security (HSTS) to specify that Firefox only connect to it securely. As a result, it is not possible to add an exception for this certificate. www.google.com.au uses an invalid security certificate. The certificate is not trusted because the issuer certificate is unknown. The server might not be sending the appropriate intermediate certificates. An additional root certificate may need to be imported. (Error code: sec_error_unknown_issuer)
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Does this also happen when you connect to the HTTPS version of this homepage?
Sorry to hear about this hassle, and thanks for the error text.
Have you seen certificate errors on other sites or is this purely an issue with Google?
If numerous sites are affected: do you use security software that filters secure connections, such as Avast, BitDefender, ESET or Kaspersky? These products need to present "fake" certificates to Firefox in order to intercept and decrypt your browsing. If you either (1) update to a new major version of that product, or (2) use Firefox's reset/refresh feature, then Firefox may no longer trust your security software to generate those fake certificates, and you need to set Firefox up to work with it again.
But another cause can be malware that hitched a ride with some software you installed recently.
To try to track down the cause, on the error page, you can visit a site such as this one and expand the third section ("I understand the risks") and click the Add Exception button. We're not going to actually save an exception yet, but this opens a dialog with a button to view the certificate so you can check on "who" or "what" signed the untrusted certificate. You can cancel out of the Add Exception dialog.
For comparison, I am attaching a screen shot where I've boxed the "Issued by" and "Certificate Hierarchy" information for this site. What does yours show?