As long as you are using default Joomla _users table and default Joomla _session table, all should work fine.
Fact, that it was working tells us it will work again.
1. If you change those options back to previous state, it starts to work?
2. What is last change you have made to your Joomla configuration? (before you figured it stopped to work)
3. If you could send an email to me with your website URL and some temporary username

assword to login to your website, we would resolve it fastest.