I am not a dreamweaver user, so I probably cannot help you with the specifics of that program usage. I try to use MySQL database whenever possible since it is designed to be used over the internet. Although Microsoft allows you to use Access on the internet, it is still not the best choice. For those times I just have to use Access database, I find that creating an ODBC DSN is the best way. I belive "custom connection string" is just Dreamweaver's lingo for DSN-less connection. I guess you can use DSN-less; it is just that I always get frustrated with them and people I know feel the same way about them.
Anyways, this might help you. I find that for troubleshooting it is good to create a "testing" connection to the database. This just bypasses all the other things that could be throwing the error messages and will at least allow you to discover if the permissions are set right.
Create an ODBC DSN Database Connection
First use your control panel to create the DSN. If you have a DSN (data source name) connection called "apples" you can connect to the database with the following ASP code:
<%
set conn=Server.CreateObject("ADODB.Connection")
conn.Open "apples"
%>
With an ODBC connection, you can connect to any database, on any computer in your network, as long as an ODBC connection is available. For this reason, I find it more secure to name my ODBC database DSN connections something more complex like apples12763.
Create a DSN-less Database Connection
Another way to connect to a database is to use a DSN-less connection. Some people find it easier but I do not, mainly because it relies on server mappath. You can use a DSN-less connection for any Microsoft Access database on your web site.
If you have a database called "apples.mdb" located in a web directory like "c:\webspace\user\domain.com\private\", you can connect to the database with the following ASP code:
<%
set conn=Server.CreateObject("ADODB.Connection")
conn.Provider="Microsoft.Jet.OLEDB.4.0"
conn.Open "c:\webspace\user\domain.com\private\apples.mdb"
%>
Take notice from the example above that you have to specify the Microsoft Access database driver (Provider) and the actual physical path to the database on your server.
So try making a test connection to your db using these examples (save the code as dbtest.asp or something like that) and if it connects there will be no message. If it cannot connect then there will be an error message displayed in the web browser. I find that for some reason, firefox browser displays more accurate error messages than IE.
Hope this helps you.