Why are a data access layer and an ORM mutually exclusive? An ORM is just an abstraction over your database. You might find use in it as a tool to access your database but contain the use of the ORM to within your data access layer.
Mind sharing an example of a large(ish) app that doesn't make use of an ORM? Last time this topic came up, I went looking for one (admittedly not too hard) and I came up empty handed.