Runtime Error '3709' while accesing SQL database in VB6

Question

I have a VB6 application which someone wrote, which does not work for only some users who try to use it.

This is the code running which returns an error:

 On Error GOTO error_handler
 ..
 Set db = New ADODB.Connection
 db.Open "Provider=SQLOLEDB.1;Persist Security Info=False;User ID=****;Password=****; Initial Catalog=***;Data Source=****,1433"
 error_handler:
 If db.Error.count then
 strDBErrors = "No access to Main Database."
 For Each err In db.errors
  strDBErrors = strDBErrors & vbCrLf & err.Description
 Next
 MsgBox strDBErrors

After this code runs, I get two Boxes of error. One which states a Runtime Error 3709, And the other which has Two lines: one of it is my Custom error message, and the second if this: "Logon Failed for user the user".

This only happens to one user on a specific computer on which this program is installed. It does not happen on any other computer with any other user. I tried reinstalling the program with that user on that computer, but it did not work.

Any ideas?