Was the DSi browser based on the same code as the DS browser?
The DS browser (which seems to be what you're talking about) was 2 physical cartridges, one that slotted into the regular DS game slot and an 8GB memory expansion cart that went in the GBA slot. The DSi's browser was built in, and the system didn't even have a GBA slot.
e: On a tangent, the Nintendo DS homebrew scene did end up with a standard (DLDI) for accessing flashcart storage, including the SD/CF slots on some GBA flashcarts -- so you would not have gotten 8 GB of RAM, but if you paid through the nose, you could potentially have made your DS swap out memory pages to an 8 GB memory card :V
The DS browser (which seems to be what you're talking about) was 2 physical cartridges, one that slotted into the regular DS game slot and an 8GB memory expansion cart that went in the GBA slot. The DSi's browser was built in, and the system didn't even have a GBA slot.