Hi,
you have to keep few things in mind.
If the application is 32bit then you have to use the 32bit driver ('Microsoft Access Driver (*.mdb)'). This driver is almost installed.
If the application is 64bit then you have to use the 64bit driver ('Microsoft Access Driver (*.mdb, *.accdb)'). This driver must be installed (for examples runtimes a post above, or MSAccess 64bit).
If I made a program then I use this following:
{$IFDEF CPU64}
ODBCDRIVER := 'Microsoft Access Driver (*.mdb, *.accdb)';
ODBCRegistryKey := 'SOFTWARE\ODBC\ODBCINST.INI\ODBC Drivers';
{$ELSE}
ODBCDRIVER := 'Microsoft Access Driver (*.mdb)';
ODBCRegistryKey := 'SOFTWARE\WOW6432Node\ODBC\ODBCINST.INI\ODBC Drivers';
{$ENDIF}
I check the Registry if the driver is available.