I vaguely remember something about NDSmail not support any encryption on the wireless at all, though I don't know if that's accurate still. Also keep in mind that it's a relatively old app, so it may be using an older version of the homebrew wifi library that doesn't support newer DS Lites.
I think you are thinking about the older versions of NDSMail couldn't use SSL to connect to Gmail (issue fixed (again) in the current version).
I've tested NDSMail (and a fair amount of other Homebrew) with a 2 year old and a 6 month old DS lite, have not got any that don't work. The only handheld compatibility problems I've seen were a long time ago when the DS Lite first came out, but all the good Homebrew has been updated.
Once you have Wi-Fi sorted (use a fixed IP and a router) all Homebrew
Personally NDS Mail works perfectely for me, I have no password but I use MAC filtering to help protect my network from the neighbours. Try that. You could use a normal ds browser such as DSOrganize or Bunjalloo to access your e-mail but NDS Mail is easier