Windows Small Business Server 2008 Standard & Sharepoint Services 3.0

The basic steps are:

1. Create a new web application in your new WSS server.
2. Follow the instructions in Move content databases between instances of SQL Server.

However you may not be able to perform all of the steps exactly as written if your previous server farm is not available. The main thing is that you get the most recent backup of the databases restored on your SQL Server, then follow these steps from the linked article:

13. In Central Administration, on the Application Management page, in the SharePoint Web Application Management section, click Content databases.

14. On the Manage Content Databases page, click Add a content database.

15. On the Add Content Database page, type the exact name of the transferred content database, and then click OK.

16. Repeat steps 14 and 15 for each database you are adding. Be sure that you select the correct Web application from the Web Application menu for each database.

I don't know your farm topology but if you are sharing the same SQL Server used for the dead server farm, make sure that the dead farm is completely powered off. You don't want two different SharePoint farms accessing the same data (especially if one is in an inconsistent state).

First, no matter what you do, you should run the SharePoint Prescan tool, to determine any possible issues you may have with upgrading. Here is a guide to running the prescan tool.

There are many different migration tools and methods to migrate from SharePoint v2 to SharePoint v3. Microsoft has a TechNet article about the different (Microsoft supported) methods available, pros and cons, and how to perform each: Determine upgrade approach [Windows SharePoint Services]. There is a SPS to MOSS version available as well.

Generally the database migration upgrade method is the easiest (assuming you are not using a lot of customizations). This involves migrating the SQL database (if necessary) and attaching it to your new SharePoint instance (either through Central Administator or with stsadm -o addcontentdb). SharePoint will upgrade the database automatically.

In place upgrade will probably not suit you, considering you are not upgrading the WSS instance, but moving the content to a new farm.

A commercial tool that I have used is metalogix SharePoint Site Migration Manager and it usually does the trick. It uses the v2 and v3 APIs to copy content from your old instance to your new instance.