Use the upgrade/migration options in Central Administration to achieve
your desired outcome. You can migrate/upgrade at the site collection
level in Central Administration.

I went through Sharepoint 3.0 Central Administration -> Operations
Tab -> Upgrade/Migrations. The options which i found as follows:
1) Microsoft Content Management Server migration
2) Enable Enterprise Features
3) Enable features on existing sites
4) Convert license type

But i couldn't get any options for upgrading wss 2.0 sites to wss 3.0

For some reason, I thought both deployments were on the same servers.
If not, then you can do a content database migration, as you mention in
your post. But since that isn't working, I'm not able to help you
troubleshoot it via email. I would suggest that you contact PSS. It
could be any number of things.