In order to get DNN working with Access you'll need to get an Access Dataprovider for DNN, I honestly don't believe one exists anymore. Back in the 2.0 days you could run DNN off of access, but I haven't seen that supported in a long time.

You would be better off trying to use SQLExpress, it's free from MS, and DNN does support SQLExpress.

A data provider is a layer in DNN that you can sub in other functionality, connections with different types of databases. There was at one point a mysql dataprovider for DNN, but it was not maintained by the core team that develops DNN. I believe there's a 4.8.4 provider available. The problem with using a custom dataprovider such as one for mysql is that the provider would be defined for the core code, and some common modules, but most third party modules wouldn't have a mysql provider available, limiting the modules you can use on your website.

While it is flexible, I always recommend to businesses that they stick with the default SQL providers for DNN simply for the ease of use for third party modules. You can develop custom mysql providers for modules, but in the long run you will most likely spend more money developing those providers than you would having simply purchased a SQL license from Microsoft.

SQLExpress is free however and definitely a viable option for smaller sites.