For one thing you don´t have an SD card, you have an MMCplus card, it even says that on the sticker. That explains why you dont have the write protection tab.
That can also explain why it doesn´t work properly. If you already tried to format it and it fails even then, it could be that the card is corrupted, a fuse is blown in the DSi or something along that.
The powerdemand for MMC+ cards are different from regular SD / MMC and some of the lowlevel stuff is pretty different, so it can simply be that the DSi doesn´t support it.
Just buy an ordinary SD card if you even need it, the smaller sizes cost less then a beer at the pub usually.