There's no user-accessible internal memory on the 60csx - I have one too and the screenshot below is what I see in Basecamp. The things that are shown in "internal storage" are just your user data (waypoints, tracks, routes), there are no system files. These aren't "files" at all, it is data that Basecamp retrieves from the device using Garmin's old protocol.
The 60csx is not like newer Garmin devices, it is not file-based. Everything that is needed to operate the GPS is included in the firmware. There's just nothing that you can do to mess with that - either it works, or it doesn't.

So I have no idea what might be wrong, maybe a problem with your memory card? Is it formatted as FAT32? Maybe try a different card? How large is the card? There are limits to how big a card these old devices can use.
There are also limits to how many map segments you can access. If you load too many maps, some of them won't work. This is actually very restrictive, so if you have a bunch of maps loaded, try removing all but one and see if that works.