Ichigosj, it's called NES DS. I don't know how you could forget a name like that.
lolzed, why bother responding if you have no clue what you're talking about? Of course you can run emulators on your DS, but they have to be written for the DS in the first place. You can't just put Project64 on your cart and expect it to run.
Now to the original poster. I'm not entirely sure why you're getting DLDI errors, as the CycloDS Evolution has had automatic DLDI patching for a long time. How old is your cart, and have you upgraded the firmware recently?
On a side note, just downloading the DLDI file isn't enough, you'd have to actually patch the *.nds file with it. The DIDI file tells the homebrew application how to interface with your card's filesystem, so if the DLDI file itself is just sitting on the filesystem, it won't do any good. But again, this is a moot point because your CycloDS should automatically be patching upon execution.