That error is nearly always caused by a bad connection string when an ADODB.connection object has its .open() method called.
For example, take the following code:
Dim SqlUsername : SqlUsername = "YOURSQLUSERNAME"
Dim SqlPassword : SqlPassword = "YOURSQLPASSWORD"
Dim ConnectionString : ConnectionString = "DRIVER={SQL Server};SERVER=YOURSERVERNAME;DATABASE=YOURDATABASENAME;UID=" & SqlUsername & ";PWD=" & SqlPassword
Dim db
Set db = Server.CreateObject("ADODB.Connection")
db.Open ConnectionString , SqlUsername , SqlPassword
Note how the connection string includes a driver identifier, in this example that is SQL Server.
Somewhere in your application you’ll have an adodb.connection.open() method being called with a connection string, you need to find it, determine the driver being used and install it on your server.
Another thing to keep in mind, some data source drivers are 32bit and if your running your website in a 64bit application pool in IIS you’ll need to allow 32bit objects – see this related question on that: Uploading picture after migration from IIS 6.0 to IIS 7.5