Your problem is within sql sintaxe as you can't compare that way at where clause.
try to change your code to this :
Private Sub Searchbtn_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Searchbtn.Click
Dim str as string = ""
Str = "Select DesignID From Design_Parameters Where ParameterValue='" & Trim(txtname.text) & "'"
ds = New DataSet()
da = New SqlClient.SqlDataAdapter(Str, conn)
da.fill(ds)
If (ds.Tables(0).Rows.Count > 0) Then
MessageBox("Record Found")
Else
MessageBox("No Record Found")
End If
End Sub