This has been happening for the last week or so.
It happens if I don't access it for a while. As long as I keep using it, it seems to work.
this didn't happen with version 3.5.6?
check your extensions and make sure they're all up-to-date.
if this doesn't help, start disabling the extensions one by one to eliminate the culprit.
if that fails: backup Firefox with FEBE (Firefox Environment Backup) or MozBackup (a backup is always handy to have anyway :), uninstall Firefox completely and reinstall it, then restore your profile, bookmarks and addons from the backup.
as a last resort, you can revert back to version 3.5.6 which you can download here.
I was also facing this problem, I suggest to just upgrade it to 3.6 version. It will become stable. I was also not able to further from my home page Google. Then, I just click help, Check for updates and Upgraded it to latest version 3.6. I don't know this is right solution or not, but it works for me.