What word should I pick for the "digital room" of a storage device, e.g. an SD memory card? And what about the preposition?
I couldn't download the file because there wasn't enough space/room/memory/capacity etc. on/in my hard drive.
The term "memory" is often used in computer contexts to mean active memory (i.e. RAM). For non-volatile data, the first thing that comes to mind is "storage", but "capacity" also works. "Space" and "room" are less specific terms, but they can also communicate the idea. Also, the term "hard drive" is generally understood to mean the main storage of a device, and usually is understood to mean magnetic storage, so you should avoid using it to refer to solid state devices such as SD memory cards. The preposition would be "on".
I think this would be the right one: There was not enough space on my hard drive.
The other words "room/memory/capacity" would not sound right.
Hard drive itself is a kind of memory like a flash drive. Room is more general and is for physical space. Capacity also refers to physical capability of something (or may be someone.)