In Chapter 2 Vivaldi is arrested and I bailed him out. Then went to his house to get the 2 books I need. He gave me the books. Then, according to the guide, I am to talk to him about the Salamandra, a conversation that is supposed to exonerate him. There is no conversation leading to his innocence. He's still a suspect!! I have no idea what I missed.

Does this mean I'm dead in the water? Can the game continue even though Vivaldi is still a suspect?

Or do I just give up on playing Witcher? (This is my second time thru Chapter 2, got stuck before.)

If you talk to Zoltan about Vivaldi, he will tell you that he no longer has control of the bank.
Then you should have the option to tell Vivaldi you don't think he's involved with salamanda.

Thank you very much. Problem solved!!!

All of these suspect quests have multiple solutions, which change depending on the order you do then and what you found out, or believed you found out.
The easiest way to find Ramsmeat "innocent" is to botch the autopsy and find Kalkstein guilty. (you'll clear him later)
Going into the crypt in the cemetery will also find Ramsmeat innocent.
If "Raymond" tells you to kill Ramsmeat, and you medallion is shaking, just leave and then go back to Raymond and let him believe you killed Ramsmeat.
Failing all that, you can just kill Ramsmeat, he may not be working with salamanda, but he's hardly innocent.
If you can't get into the cemetery because you accused Vincent and he's pissed with you, go to Shani's and you'll find out Thaler is innocent and he will clear the gravediggers dept.