Oh, and one more thought...
If you're on Fx 26 or later, you might try
about:networking -> DNS
check "autorefresh every 3 seconds"
if mail.google.com isn't listed there, try again to get to Gmail as you did in the OP
look at what IP address(es) is listed for mail.google.com in about:networking
It's possible that something is screwed up with only Fx... in which case you should try Standard Diagnostic (and maybe scan your system for malware?).
If you're on Fx 26 or later, you might try
about:networking -> DNS
check "autorefresh every 3 seconds"
if mail.google.com isn't listed there, try again to get to Gmail as you did in the OP
look at what IP address(es) is listed for mail.google.com in about:networking
It's possible that something is screwed up with only Fx... in which case you should try Standard Diagnostic (and maybe scan your system for malware?).