Yours first sentence was:
Can anyone tell me the code to open a table in an Access database using code only?...

OK, you can put connection string into the ADODC control's ConnectionString property (assuming adodc1 is ADODC control):

adodc1.ConnectionString = "Provider=Microsoft.Jet.OLEDB.4.0;Data Source=C:\Program Files\Microsoft Visual Studio\VB98\NWIND.MDB;Persist Security Info=False"
adodc1.Refresh

This code assumes also that all data bound controls are bound to ADODC control at design-time and you set all other necessary properties of ADODC control also at design-time.

Again, you must change connection string to your own path to database and use in it App.Path.