This is late - however, potentially useful for others in the future.
Long story short - you can't delete files that have been added to the memory via computer!
All the information, including that found on the official Garmin instructions online indicate that this must be done through a computer connection.
However (I can't test this as I don't have a device) it seems that all user data can be deleted by doing a factory reset, which should take the device back to the settings as it was when it came out of the box when you first bought it.
To do a factory reset: Performed at users own risk!
- press and hold the "enter" button
- press the "power/light" button
- wait for the "Do you want to delete all user data" message
- select "Yes"
Note that this will delete all waypoints, etc - anything that you have added to the device since getting it. I think internally stored maps (i.e. OEM supplied) will still be there, but perform at your own risk.