So you can use the AR, but not go online.
Seems like Nintendo is starting to crack down on AR use. Older models obviously do not recognize it, but they've set newer models to do so. They don't forbid you to use it, they just forbid you to go online WHILE using it as you could be cheating and using hacked Pokémon or something.
That's my take on why it wouldn't work, but you could always pose this question in the proper forum as well. I don't try to connect with my used older-model DS (besides, it can't), so I can't confirm anything else as far as going online, so this is just a guess.
Of course, yes, delete the games you don't use. That would be the best thing to do first.