This doesn't seem to be an access point problem.
For up to about a month after Pokemon X & Y came out, I was able to connect to my access point and the internet easily and all automatically. I played lots of online battles with both friends and passersby, and Wondertrade worked fantastically. Then, it just stopped. I could no longer connect to my home router, and living in the boonies, I didn't know anyone else with an access point that I cared to try it out on (and I misplaced Pokemon X), so my 3DS went unused for a long time. I picked it up again last month, and found I still couldn't connect to my access point. I fiddled with it, manually setting up a new connection to my router and manually added all of the IP, Subnet Mask, Gateway, and DNS information, and Voilà! I could connect to my access point! However, I still can't connect to the internet, even with full signal.
My router is an SMC Gateway, setup with a WPA-PSK (AES) encryption. Yes, the password is entered correctly.
It also seems to be giving me the 003-2101 error code, but... My computer, connected wirelessly, is connecting fine, my roku is wirelessly connecting to it fine and in use streaming Netflix perfectly at this very moment, and they are the only other devices connect to it right now. The DNS settings are entered correctly, and I'm not using a proxy.
I have no idea why it could be giving me that error code. It couldn't be a signal problem unless something totally unknown is interfering with the connect that didn't exist before, or something about my router is just not the same that occurred when my internet provider updated their systems.
Any help other than links to error pages would be appreciated, because I've been pouring over the 3DS support pages for a few days, and I think my eyes are about ready to start bleeding... though, if you honestly feel like I've missed something that might help, I'd probably still appreciate that too!
Thank you kindly!