I'm not a specialist and I think it's hard to tell in general which values are right and which are wrong, you'll have to find this yourself. If you google, you'll find the ways how to correct those values.
There is also another way that I used to locate the problem:
- Install fresh prestashop in a test site, e.g test.yourdomain.com
- If cart works correctly on fresh installation, copy production database to test site. If it stops working then, you'll know the problem in somewhere in DB.
- Overwrite test DB with fresh data again and copy table group by table group from production DB and you'll locate the problematic table and data.
Be careful, the above procedure is not explained in detail, and there is no guarantee that it will produce result. Anyway, maybe will give somebody an idea how to locate a problem on site, not only with empty cart. It worked for me...