|This page uses an answer system that is currently obsolete.
The comment system should be used if another answer should be added.
If your DSi connects to the internet but your games won't, then it should provide an error code when your game doesn't. Go to Nintendo's official website and type in the error code and it should give an answer to your question. If that doesn't work, e-mail Nintendo directly.
Also, if your router is encrypted with WPA, the DSi will connect to the internet (for stuff like DSi Shop and Browser) but games cannot utilize that. They can, however, be played with a WEP encryption.